Skip to main content

Full text of "Transactions of the Royal Society of Edinburgh"

See other formats


TRANSACTIONS 



OF THE 



ROYAL SOCIETY 



OF 



EDINBURGH. 



VOL. XXIV. 



EDINBURGH: 

PUBLISHED BY ROBERT GRANT & SON, 82 PRINCES STREET. 
AND WILLIAMS & NORGATE, 14 HENRIETTA STREET, COVENT GARDEN, LONDON. 



MDCCCLXVII. 



TRANSACTION S 



01' THE 



ROYAL SOCIETY 



OF 



EDINBURGH. 



VOL. XXIV. 



EDINBURGH: 

PUBLISHED BY ROBERT GRANT & SON, 82 PRINCES STREET. 
AND WILLIAMS & NORGATE, 14 HENRIETTA STREET, COVENT GARDEN, LONDON. 



MDCCCLXVII. 



-'J 



a rt* 



THE KEITH, BEISBANE, AND NEILL PEIZES. 



The above Prizes will be awarded by the Council in the following manner : — 

I. KEITH PRIZE, 

The Keith Prize, consisting of a Gold Medal and from £40 to £50 in Money, 
will be awarded in the Session 1867-68, for the " best communication on a 
scientific subject, communicated, in the first instance, to the Royal Society dur- 
ing the Sessions 1865-66 and 1866-67." Preference will be given to a paper 
containing a discovery. 

II. MAKDOUGALL BRISBANE PRIZE. 

This Prize is to be awarded biennially by the Council of the Royal Society of 
Edinburgh to such person, for such purposes, for such objects, and in such manner 
as shall appear to them the most conducive to the promotion of the interests of 
science ; with the proviso that the Council shall not be compelled to award the 
Prize unless there shall be some individual engaged in scientific pursuit, or some 
paper written on a scientific subject, or some discovery in science made during 
the biennial period, of sufficient merit or importance in the opinion of the Council 
to be entitled to the Prize. 

1. The Prize, consisting of a Gold Medal and a sum of Money, will be awarded 
at the commencement of the Session 1868-69, for an Essay or Paper having 
reference to any branch of scientific inquiry, whether Material or Mental. 

2. Competing Essays to be addressed to the Secretary of the Society, and 
transmitted not later than 1st June 1868. 

3. The competition is open to all men of science. 

4. The Essays may be either anonymous or otherwise. In the former case, 
they must be distinguished by mottoes, with corresponding sealed billets super- 
scribed with the same motto, and containing the name of the Author. 

VOL. XXIV. PART III. b 



VI 



5. The Council impose no restriction as to the length of the Essays, which may 
be, at the discretion of the Council, read at the Ordinary Meetings of the Society. 
They wish also to leave the property and free disposal of the manuscripts to the 
Authors ; a copy, however, being deposited in the Archives of the Society, unless 
the Paper shall be published in the Transactions. 

6. In awarding the Prize, the Council will also take into consideration any 
scientific papers presented to the Society during the Sessions 18G6-G7 and 
1867-68, whether they may have been given in with a view to the Prize or not. 

III. NEILL PRIZE. 

The Council of the Royal Society of Edinburgh having received the bequest of 
the late Dr Patrick Neill of the sum of £500, for the purpose of " the interest 
thereof being applied in furnishing a Medal or other reward every second or third 
year to any distinguished Scottish Naturalist, according as such Medal or reward 
shall be voted by the Council of the said Society," hereby intimate, 

1. The Neill Prize, consisting of a Gold Medal and a sum of Money, will 
be awarded at the commencement of the Session 1868-G9. 

2. The Prize will be given for a Paper of distinguished merit, on a subject of 
Natural History, by a Scottish Naturalist, which shall have been presented to 
the Society during the three years preceding the 1st May 1868, — or failing 
presentation of a Paper sufficiently meritorious, it will be awarded for a work 
or publication by some distinguished Scottish Naturalist, on some branch of 
Natural History, bearing date within five years of the time of award. 



Vll 



AWARDS OF THE KEITH, MAKDOUGALL BRISBANE, AND NEILL PRIZES, 

SINCE 1862. 



AWARD OF THE KEITH PRIZE. 



19th Biennial Period, 1863-65. Principal Forbes, St Andrews, for his " Experimental Inquiry 

into the Laws of Conduction of Heat in Iron Bars," 
published in the Transactions of the Society. 



MAKDOUGALL BRISBANE PRIZE. 



4th Biennial Period, 1864-66. Not awarded. 



AWARD OF THE NEILL PRIZE. 



3d Triennial Period, 1862-65. Andrew Crombie Ramsay, F.R.S., Professor of Geology in 

the Government School of Mines, and Local Director of 
the Geological Survey of Great Britain, for his various 
works and memoirs published during the last five years, 
in which he has applied the large experience acquired by 
him in the Direction of the arduous work of the Geological 
Survey of Great Britain to the elucidation of important 
questions bearing on Geological Science. 



DIRECTIONS TO THE BINDER FOR PLACING THE PLATES IN THIS VOLUME. 



Plate 



Illustrating Principal James D. Forbes' Paper on an Experimental 
Inquiry into the Laws of the Conduction of Heat in Bars. Part 
II. On the Conductivity of Wrought Iron deduced from the Expe- 
riments of 1851, ..... To face 'page 



Illustrating Mr Edward Bang's Paper on the Contact of the Loops of 
Epicycloid al Curves, . . 



XXII. 



XXIII. -j 

XXIV. f 
XXV. t 

xxvi. r 

XXVII. \ 

xxviii. L 

XXIX. f 
XXX. I 

XXXI. j 
XXXII. 1 

XXXIII. 

XXXIV. ) 

XXXV. [■ 

XXXVI. 1 



Illustrating Mr Alexander Buchan's Paper on an Examination of 
the Storms of Wind which occurred in Europe during October, 
November, and December 1863, . 



Illustrating Sir David Brewster's Paper on the Bands formed by the 
Superposition of Paragenic Spectra produced by the Grooved Sur- 
faces of Glass and Steel- Part I. , . 

Illustrating Sir David Brewster's Paper on the Bands formed by the 
Superposition of Paragenic Spectra produced by the Grooved Sur- 
faces of Glass and Steel. Part II., ..... 

Illustrating Sir David Brewster's Paper, Report on the Hourly Meteor- 
ological Register kept at Leith Fort, in the years 1826 and 1827, 

Illustrating Professor C. Piazzi Smyth's Paper, Notice of Recent 
Measures at the Great Pyramid, and some Deductions flowing 
therefrom, ........ 

Illustrating Dr W. Lauder Lindsay's Paper, Observations on New 
Lichens and Fungi collected in Otago, New Zealand, 

Illustrating Dr John Alexander Smith's Paper, Description of Cala- 
moichthys, a new Genus of Ganoid Fish from Old Calabar, Western 
Africa, forming an addition to the Family Polypterini, 

Illustrating Sir David Brewster's Paper on theColours of the Soap-Bubble, 

Illustrating Sir David Brewster's Paper on the Figures of Equilibrium in 
Liquid Films, ....... 



{Illustrating the Rev. Thomas Brown's Paper on the Arctic Shell-Clay 
of Elie and Errol, viewed in connection with our other Glacial and 
more recent Deposits, ...... 

VOL. XXIV. PAET III. C 



73 



121 



191 



221 

227 
351 

385 

407 

457 
491 

505 
617 



DIRECTIONS TO THE BINDER FOR PLACING THE PLATES. 



Plate XXXVIII 



Illustrating Sir David Brewster's Paper, Description of a Double 
Holophote Apparatus for Lighthouses, and of a Method 
( of Introducing the Electric and other Lights, To face page 

( Illustrating Sir David Brewster's Paper, on the Motions and 

XXXIX. \ Colours upon Films of Alcohol and Volatile Oils, and other 

( Fluids, ....... 



XL. 

XLI. 

XLII. 

XLIII | 

XLIV.J 

XLvJ 



Illustrating Mr John Allan Broun's Paper on the Diurnal Vari- 
ation of the Magnetic Declination near the Magnetic 
Equator, and in both Hemispheres, .... 

Illustrating Dr Ramsay H. Traquair's Paper, Description of 
Pygopterus Greenockii (Agassiz), with Notes on the Struc- 
tural Relations of the Genera Pygopterus, Amblypterus, and 
Eurynotus, ....... 



635 



653 



669 



701 



LAWS 



OF THE 



ROYAL SOCIETY OF EDINBURGH, 



AS REVISED 31st OCTOBER 1866. 



LAWS. 



[By the Charter of the Society (printed in the Transactions, Vol. VI. p. 5), the Laws cannot 
be altered, except at a Meeting held one month after that at which the Motion for 
alteration shall have been proposed.] 

I. 

THE ROYAL SOCIETY OF EDINBURGH shall consist of Ordinary and Title. 
Honorary Fellows. 

II. 

Every Ordinary Fellow, within three months after his election, shall pay Two The fees of Ordi- 

.. imi m ' i .. nal 7 Fellows resid 

Guineas as the fee of admission, and Three Guineas as his contribution for the mg in Scotland. 
Session in which he has been elected ; and annually at the commencement of every 
Session, Three Guineas into the hands of the Treasurer. This annual contribution 
shall continue for ten years after his admission, and it shall be limited to Two 
Guineas for fifteen years thereafter.* 

III. 

All Fellows who shall have paid Twenty-five years' annual contribution shall Payment to cease 

after 25 years. 

be exempted from farther payment. 

IV. 

The fees of admission of an Ordinary Non-Resident Fellow shall be £26, 5s., Fees of Non-Kesi- 

, J ' ' dent Ordinary 

payable on his admission ; and in case of any Non-Resident Fellow coming to Fellows. 

reside at any time in Scotland, he shall, during each year of his residence, pay the 

usual annual contribution of £3, 3s., payable by each Resident Fellow ; but afte T 

payment of such annual contribution for eight years, he shall be exempt from any 

farther payment. In the case of any Resident Fellow ceasing to reside in Scot- be^mfn^Non-Re 



sident. 



* At the Meeting of the Society, on the 5th January 1857, when the reduction of the Contri- 
butions from £3, 3s., to £2, 2s., from the 11th to the 25th year of membership, was adopted, it was 
resolved that the existing Members shall share in this reduction, so far as regards their future 
Annual Contributions. 

A modification of this rule, in certain cases, was agreed to 3d January 1831. 

VOL. XXIV. PART III. d 



XIV 



land, and wishing to continue a Fellow of the Society, it shall be in the power of 
the Council to determine on what terms, in the circumstances of each case, the 
privilege of remaining a Fellow of the Society shall be continued to such Fellow 
while out of Scotland. 



Defaulters. 



V. 



Members failing to pay their contributions for three successive years (due 
application having been made to them by the Treasurer) shall be reported to the 
Council, and, if they see fit, shall be declared from that period to be no longer 
Fellows, and the legal means for recovering such arrears shall be employed. 



VI. 

OrSaTVeiiows None but Ordinary Fellows shall bear any office in the Society, or vote in the 

choice of Fellows or Office-Bearers, or interfere in the patrimonial interests of the 
Society. 



Numbers Un- 
limited. 



VII. 

The number of Ordinary Fellows shall be unlimited. 



Fellows entitled 
to Transactions. 



VIII. 

The Ordinary Fellows, upon producing an order from the Treasurer, shall be 
entitled to receive from the Publisher, gratis, the Parts of the Society's Trans- 
actions which shall be published subsequent to their admission. 



Mode of Recom- 
mending Ordinary 
Fellows. 



IX. 

No person shall be proposed as an Ordinary Fellow without a recommenda- 
tion subscribed by One Ordinary Fellow, to the purport below.* This recom- 
mendation shall be delivered to the Secretary, and by him laid before the Council, 
and shall afterwards be printed in the circulars for three Ordinary Meetings of 
the Society, previous to the day of the election, and shall lie upon the table during 
that time. 



Honorary Fellows, 
British and 
Foreign. 



X. 

Honorary Fellows shall not be subject to any contribution. This class shall 

* " A. B., a gentleman well skilled in several brandies of Science (or Polite Literature, as the case 
" may be), being to my knowledge desirous of becoming a Fellow of tbe Royal Society of Edin- 
" burgh, I hereby recommend him as deserving of that honour, and as likely to prove a useful and 
" valuable Member." 

This recommendation to be accompanied by a request of admission signed by the Candidate. 



XV 

consist of persons eminently distinguished for science or literature. Its number 
shall not exceed Fifty-six, of whom Twenty may be British subjects, and Thirty- 
six may be subjects of foreign states. 

XI. 

Personages of Royal Blood may be elected Honorary Fellows, without regard E °y al Personages. 
to the limitation of numbers specified in Law X. 

XII. 

Honorary Fellows may be proposed by the Council, or by a recommendation Recommendation 
(in the form given below*) subscribed by three Ordinary Fellows ; and in case lows, 
the Council shall decline to bring this recommendation before the Society, it shall 
be competent for the proposers to bring the same before a General Meeting. The 
election shall be by ballot, after the proposal has been communicated viva voce Mode of Election. 
from the Chair at one meeting, and printed in the circular for the meeting at 
which the Ballot is to take place. 

XIII. 

The election of Ordinary Fellows shall take place at the Ordinary Meetings of Election of Ordi- 

ml . navy Fellows. 

the Society. The election shall be by ballot, and shall be determined by a majo- 
rity of at least two-thirds of the votes, provided Twenty-four Fellows be present 
and vote. 

XIV. 

The Ordinary Meetings shall be held on the first and third Mondays of every Ordinary Meet- 
month from November to June inclusive. Regular Minutes shall be kept of the 
proceedings, and the Secretaries shall do the duty alternately, or according to such 
agreement as they may find it convenient to make. 

XV. 

The Society shall from time to time publish its Transactions and Proceedings. The Transactions. 
For this purpose the Council shall select and arrange the papers which they shall 

* We hereby recommend 

for the distinction of being made an Honorary Fellow of this Society, declaring that each of us from 
our own knowledge of his services to {Literature or Science, as the case may be) believe him to be 
worthy of that honour. • 

(To be signed by three Ordinary Fellows.) 



To tlie President and Council of Royal Society 
of Edinburgh. 



XVI 



deem it expedient to publish in the Transactions of the Society, and shall super- 
intend the printing of the same. 



How Published. 



The Council. 



XVI. 

The Transactions shall be published in Parts or Fasciculi at the close of each 
Session, and the expense shall be defrayed by the Society. 

There shall be elected annually, for conducting the publications and regulating 
the private business of the Society, a Council, consisting of a President ; Six Vice- 
Presidents, two at least of whom shall be resident ; Twelve Councillors, a General 
Secretary, Two Secretaries to the Ordinary Meetings, a Treasurer, and a Curator 
of the Museum and Library. 



XVII. 
Retiring Council- Four Councillors shall go out annually, to be taken according to the order in 

which they stand on the list of the Council. 



Election of Officc- 
Bearors. 



XVIII. 

An Extraordinary Meeting for the Election of Office-Bearers shall be held on 
the fourth Monday of November annually. 



Special Meetings ; 
how called. 



XIX. 

Special Meetings of the Society may be called by the Secretary, by direction 
of the Council ; or on a requisition signed by six or more Ordinary Fellows. 
Notice of not less than two days must be given of such Meetings. 



XX. 

Treasurer's Duties. The Treasurer shall receive and disburse the money belonging to the Society, 
granting the necessary receipts, and collecting the money when due. 

He shall keep regular accounts of all the cash received and expended, which 
shall be made up and balanced annually ; and at the Extraordinary Meeting in 
November, he shall present the accounts for the preceding year, duly audited. At 
this Meeting, the Treasurer shall also lay before the Council a list of all arrears 
due above two years, and the Council shall thereupon give such directions as 
they may deem necessary for recovery thereof. 



Auditor. 



XXI. 

At the Extraordinary Meeting in November, a professional accountant shall 
be chosen to audit the Treasurer's accounts for that year, and to give the necessary 
discharge of his intromissions. 



XV11 

XXII. 

The General Secretary shall keep Minutes of the Extraordinary Meetings of J^ e e r 3 al Secretar y' s 
the Society, and of the Meetings of the Council, in two distinct books. He shall, 
under the direction of the Council, conduct the correspondence of the Society, and 
superintend its publications. For these purposes, he shall, when necessary, employ 
a clerk, to be paid by the Society. 

The Secretaries to the Ordinary Meetings shall keep a regular Minute-book, in £ e j retarie * *° 

J ° r o Ordinary Meetings. 

which a full account of the proceedings of these Meetings shall be entered ; they 
shall specify all the Donations received, and furnish a list of them, and of the 
donors' names, to the Curator of the Library and Museum : they shall likewise 
furnish the Treasurer with notes of all admissions of Ordinary Fellows. They 
shall assist the General Secretary in superintending the publications, and in his 
absence shall take his duty. 

XXIII. 

The Curator of the Museum and Library shall have the custody and charge of Curator of Museum 

J m J ° and Library. 

all the Books, Manuscripts, objects of Natural History, Scientific Productions, and 
other articles of a similar description belonging to the Society ; he shall take an 
account of these when received, and keep a regular catalogue of the whole, which 
shall lie in the Hall, for the inspection of the Fellows. 

XXIV. 

All Articles of the above description shall be open to the inspection of the Use of Museum 

x L and Library. ' 

Fellows at the Hall of the Society, at such times and under such regulations, as 
the Council from time to time shall appoint. 

XXV. 

A Register shall be kept, in which the names of the Fellows shall be enrolled Register Book 
at their admission, with the date. 



VOL. XXIV. PART III. 



LIST OF THE ORDINAKY FELLOWS OF THE SOCIETY. 



N.B. — Those marked * are Annual Contributors. 



1846 *Alex. J. Adie, Esq., llockville, Linlithgow 

1866 *0ol. Sir James E. Alexander of Westcrton 

1867 *Rev. Dr \V. Lindsay Alexander, 17 Brown Square 

1848 Dr James Allan, Inspector of Hospitals, Portsmouth 
1856 *Dr G. J. Allman (Secretary), Professor of Natural 

History, 21 Manor Place 

1849 *David Anderson, Esq., Moredun, Edinburgh 

1845 *Dr Thomas Anderson, Prof. Chemistry, Univ., Glasgow 
1823 Warren Hastings Anderson, Esq., Isle of Wight 
1867 *Thomas Annandale, Esq., 3 Hope Street 
1840 James Anstruther, Esq., W.S. 10 

1832 *T. C. Archer, Esq., Director of the Museum of Science 
and Art, 9 Argyle Square 

1849 *His Grace the Duke of Argyll (Hon. Vice-President), 

Inverary Castle 
1822 Dr G. Walker Arnott, Prof. Botany, Univ., Glasgow 
1820 Charles Babbage, K.H., London 

1843 David Balfour, Esq., Trenaby 

1835 Dr J. H. Balfour (General Secretary), Professor of 

Medicine and Botany, 27 Inverleith Row 
1867 *George F. Barbour, Esq., 11 George Square 

1862 *Hon. Lord Barcaple, 3 Ainslie Place 
1830 Dr Thomas Barnes, Carlisle 

1858 Edmund Chisholm Batten, M.A., Lincoln's Inn, London 20 

1844 *Dr Begbie, 10 Charlotte Square 

1843 Dr Bennett, Professor of Institutes of Medicine, 1 Glen- 
finlas Street 

1861 *George Berry, Esq., 2 Windsor Terrace, Portobello 

1866 *Adara Black, Esq., 38 Drummond Place 

1850 *Hugh Blackburn, Esq., Prof. Mathematics, University, 

Glasgow. 

1863 * Professor Blackie, 24 Hill Street 

1857 *John Blackwood, Esq., 3 Randolph Crescent 

1862 *Rev. Dr VV. G. Blaikie, Pilrig Manse 
1854 Ernest Bonar, Esq. 

1863 *William Brand, Esq., 5 Northumberland Street 30 
1808 Principal Sir D. Brewster, K.U., (President), 

College 

1864 *Dr Alex. Crum Brown, 4 Rillbank Terrace 

1859 *l>r John Brown, 23 Rutland Street 
1861 *Rev. Thomas Brown, 16 Carlton Street 
1835 William Brown, Esq., 25 Dublin Street 
1861 *W. A. F. Browne, Esq., Post-Office Buildings 

1867 *A. H. Bryce, Esq., D.C.L., LL.D., 13 Salisbury Road 

1856 *David Bryce, Esq., Architect, 131 George Street 
1833 His Grace the Duke of Buccleuch, E.G., Dalkeith Palace 

1857 *Dr W. M. Buchanan, 3 Carlton Terrace 40 

1845 *I)r Burt, 88 George Street 

1847 *J. H. Burton, LL.D., Advocate, Craig House 
1863 *Robert Campbell, Esq., Advocate 



1865 *Alfred R. Catton, B.A., College 

1866 *David Chalmers, Esq., Kate's Mill, Slateford 
1840 Robert Chambers, LL.D., St Andrews 

1860 * William Chambers, Esq. of Glenormiston, 13 Chester Street 

1862 *Henry Cheyne, Esq., W.S., 6 Royal Terrace 

1823 Dr Christison, Professor of Materia Medica (Vice-Pre- 
sident), 40 Moray Place 

1863 Dr H. F. C. Cleghorn, Madras 50 
1856 *Thomas Cleghorn, Esq., Advocate, 26 Queen Street 
1812 Right Hon. Sir George CJerk, Bart., Penicuik House 
1844 Dr Thomas R. Colledge, Lauriston House, Cheltenham 
18-9 The Right honourable Lord Colonsay, London 

1829 A. Colyar, Esq. 

1850 *Dr James Scarth Combe, 36 York Place 

1866 *Thomas Constable, Esq., 11 Thistle Street 
1843 Dr John Rose Cormack, Orleans, France. 

1843 Andrew Coventry, Esq., Advocate, 29 Moray Place 

1803 *Charles Cowan, Esq., Valleyfield, Penicuik 60 

1854 *Sir James Coxe, M.D., Kinellan 

1830 J. T. Gibson-Craig, Esq., W.S., 24 York Place 
1829 Sir William Gibson-Craig, Bart., Riccarton 
1853 Rev. John Gumming, D.D., London 

1852 *James Cunningham, Esq., W.S., 50 Queen Street 

1823 Liscombe J. Curtis, Esq., Iugsdown House, Devonshire 

1851 *E. W. Dallas, Esq., 125 Princes Street 

1841 James Dalmahoy, Esq., 9 Forres Street 

1852 *Allen Dalzell, M.D., The Lodge, North Berwick 

1862 ^Nicholas Alexander Dalzell, Esq., Bombay 70 

1867 "David Davidson, Esq., Bank of Scotland 
1848 *Henry Davidson, Esq., Muirhouse 

1842 Dr John Davy, Lesketh How, Ambleside 
1867 Henry Dircks, Esq., C.E., London 

1867 ^Francis Deas, Esq., LL.B., Advocate, 32 Heriot Row 

1863 *W. Dittmar, Esq., College 

1867 *James Donaldson, Esq., LL.D., 8 Mayfield Street 

1866 *David Douglas, Esq., 11 Salisbury Road 

1839 Francis Brown Douglas, Esq., Advocate, 21 Moray PI. 

1867 *G. Stirling Home Drummond, Blair-Drummond 80 
1860 ^Patrick Dudgeon, Esq. of Cargen 

1863 *Dr J. Matthews Duncan, 30 Charlotte Square 

1851 *Sir David Dundas, Bart, of Dunira 

1863 *The Right Hon. Lord Dunfermline, Colinton House 
1859 *Rev. Dr John Duns, 2 Mansion-House Road, Grunge 
1866 *Dr James Dunsmure, 53 Queen Street 

1864 *Professor Robert Dyce, Aberdeen 

1856 *W. Mitchell Ellis, Esq., AVellington Lodge, Portobello 

1855 Robert Etheridge, Esq., Clifton, Bristol 

1866 *WilIiam Euing, Esq., Glasgow 90 

1863 *J. 1). Everett, Esq., M.A., Glasgow 

18o6 *' James Falshaw, Esq., C.B., 26 Castle Street 



XX 



1859 *Dr Fayrer, Professor of Surgery, Calcutta 

1858 Frederick Field, Esq., Chili 

1852 Dr Andrew Fleming, H.M.I.S., Bengal 

1831 Principal Forbes (Vice-President), St Andrews 

1859 Major James George Forlong, Bombay 
1828 John Forster, Esq., Liverpool 

1864 *Dr John Foulerton, Manila 

1858 *Professor Fraser, 20 Chester Street 100 
18G7 *Dr Thomas R. Fraser, College 

1867 *Frederick Fuller, Esq., Prof. Math., Univ., Aberdeen 

1867 Dr Charles Gainer, Oxford 

1867 *Dr Arthur Gamgee, 27 Alva Street 

1861 *Archibald Geikie, Esq., 16 Duncan Street, Newington 
1845 *L. D. B. Gordon, Esq., C.E., London 

1850 *Lieut-Col. W. D. Gosset, R.E. 

1867 *Dr Andrew Graham, R.N., 35 Melville Street 

1851 *Rev. Dr James Grant, 18 Great King Street 

1824 Dr Robert E. Grant, Prof. Comp. Anat., Univ. Coll., 
London 110 

1860 *Dr Frederick Guthrie, M.A., Prof, of Chemistry, Roy. 

Coll., Mauritius 

1867 *Dr D. R. Haldane, 22 Charlotte Square 

1867 *Frederick Hallard, Esq., Advocate, 7 Whitehouse Ter- 
race 

1867 *James H. B. Hallen, Esq. 

1833 Alexander Hamilton, LL.B., W.S., The Elms, Whitehouse 
Loan 

1824 Dr Robert Hamilton, 11 North Merchiston Place 
1837 Dr P. D. Handyside, 11 Hope Street 

1864 *Kev. Dr Hannah, Glenalmond 

1854 Professor Robert Harkness, Queen's College, Cork 

1867 *Sir George Harvey, 21 Regent Terrace 120 

1859 *G. \V. Hay, Esq. of Whiterigg 

1855 *James Hay, Esq., 5 Links Place, Leith 

1862 *Dr James Hector, New Zealand 

1854 Dr William Bird Herapath, Bristol 

1859 Lieut. John Hills, Bombay Engineers 

1S28 David Milne Home, Esq. of Wedderburn (VICE-PRESI- 
DENT), 10 York'Place 

1839 Dr Adam Hunter, 18 Abercromby Place 

1864 *Kobert Hutchison, Esq., Carlowrie Castle 

1855 *The Right Hon. John Inglis, Lord Justice-General, 30 

Abercromby Place 

1858 *Professor Innes(VlCE-PRESlDENT), Inverleith House 130 

1840 Edward J. Jackson, Esq., 6 Coates Crescent 

1863 William Jameson, Esq., Surgeon-Major, Saharunpore 

1860 *George A. Jamieson, Esq., 58 Melville Street 

1825 Sir William Jardine, Bart., LL.D., of Applegarth, Jardine 

Hall, Lockerby 

1865 *Charles Jenner, Esq., Easter Duddingston Lodge 
1863 *Hon. Charles Baillie, LL.D., Lord Jerviswoode, 10 

Strathearn Road 

1850 *Alex. K. Johnston, LL.D., March-Hall Park, Dalkeith 

Road 

1867 *F. B. Johnston, Esq , 9 Claremont Crescent 

1867 *\Villiam Keddie, Esq., Glasgow. 

1866 *Dr Alexander Keiller, 21 Queen Street 140 
1839 Rev. Professor Kelland 20 Clarendon Crescent 

1863 *Uharles Lawson, Esq., 35 George Square 

1865 *Charles Lawson, jun., Esq., 34 George Square 



1856 *Dr Laycock, Professor of the Practice of Medicine, 13 

Walker Street 

1853 *Rev. Dr Robert Lee, Professor of Biblical Criticism, 24 
George Square 

1863 *Hon. G. Waldegrave Leslie, 4 Heriot Row 
1858 *James Leslie, Esq., C.E., 2 Charlotte Square 
1861 *Dr W. Lauder Lindsay, Gilgal, Perth 

1864 *\Villiam Lindsay, Esq., Hermitage-Hill House, Leith 

1857 Thomas Login, Esq., C.E., Pegu 150 
1861 *Professor Lorimer, Advocate, 21 Hill Street 

1849 *Dr W. H. Lowe, Balgreen, Slateford 

1855 *Dr Stevenson Macadam, 25 Brighton Place, Portobello 
1861 *Dr James M'Bain, R.N., Logie Villa, York Road, Trinity 
1867 *John M. M'Candlish. Esq., 4 Doune Terrace 

1866 *John M'Culloch, Esq., Banker, 11 Duke Street 

1820 Dr Win. Macdonald, Prof. Civ. and Nat. Hist., St Andrews 

1847 *W. Macdonald Macdonald, Esq., t«t Martins 

1860 *Professor MacDougall, 9 Buckingham Terrace 

1861 *Dr A. E. Mackay, R.N. 160 
1840 John Mackenzie, Esq., 11 Abercromby Place 

1843 Dr A. Douglas Maclagan (Curator), Prof, of Medical 

Jurisprudence, 28 Heriot Bow 
1853 Lieut.-Col. R. Maclagan, Royal Engineers, Bengal 

1864 *Peter M'Lagan, Esq. of Pumpherston, M.P. 

1866 *John Macnair, Esq., 33 Moray Place. 

1840 Sir John M'Neill, G.C.B., Granton House 

1834 Patrick Boyle Mure Macredie, Esq., Perceton 

1858 *Dr R. B. Malcolm, 126 George Street 

1838 Thomas Mansfield, Esq., 23 Abercromby Place 

1828 Dr Manson, Nottingham 170 

1864 *J. D. Marwick, Esq., 10 Bellevue Crescent 
1866 *Professor Uavid Masson, 3 Rosebery Crescent 

1856 *James Clerk Maxwell, Esq., late Prof. Nat. Phil., King's 

College, London 

1849 *Sir William Stirling-Maxwell, Bart., Keir, M.P. 

1835 R. Mayne, Esq., 3 Merchiston Place 
1863 *Edward Meldrum, Esq., Bathgate 

1853 *Gra;me Reid Mercer, Esq., Ceylon Civil Service 

1841 John Miller, Esq., C.E., 2 Melville Crescent 
1818 Dr P. Miller, Exeter 

1852 *Thomas Miller, Esq., A.M., LL.D., Rector, Perth 

Academy 180 

1833 Rear-Admiral Sir Alexander Milne, R.N., Inveresk 

1866 *Dr Arthur Mitchell, 6 Laverock Bank Villas 

1843 *Joseph Mitchell, Esq., C.E., Inverness 

1865 *Dr John Moir, 52 Castle Street 

1866 *Dr Charles Morehead, 34 Melville Street 
1S66 *Kight Rev. Bishop Morrell, Greenhill House 
1861 *John Muir, D.C.L., LL.D., 16 Regent Terrace 
1824 Rev. Dr William Muir, Ormslie Villa, Mu-rayfield 

1857 *Dr John Ivor Murray, Colonial Surgeon, Hong Kong 

1850 Dr Sheridan Muspratt, Liverpool 190 

1842 Robert Nasmyth, Esq., 5 Charlotte Square 

1856 *Hon. Lord Neaves (Vice-President), 7 Charlotte 

Square 

1866 *Thomas Nelson, Esq., Abden House, Prestonfield 

1847 *James Nicol, Esq., Prof. Nat. Hist., Aberdeen 

1860 *Rev. Leonard Shafto Orde 

1863 *Hon. Lord Ormidale, 14 Moray Place 

1863 *David Pa K e, LL.D., 44 Gilmore Place 



XXI 



1837 Dr Richard Parnell, 7 James' Place, Leith 

1863 *Dr Alexander Peddie, 15 Rutland Street 

1856 *Dr Penny, Glasgow 200 

1849 *W. Pirrie, Esq., Prof. Surg., Marischal Coll., Aberdeen 

1859 *Dr Lyon Playfair, C.B., LL.D. (Vice-President), Prof. 

Chemistry, 14 Abercromby Place 
1834 Mungo Ponton, Esq., W.S., Clifton, Bristol 
1852 Eyre B. Powell, Esq., Madras 

1865 *James Powrie, Esq., Reswallie, Forfar 

1849 *Hon. B. P. Primrose, 22 Moray Place 

1827 Very Rev. E. B. Ramsay, LL.D., 23 Ainslie Place 

1850 *W. J. M. Rankine, Esq., C.E., Prof. Civil Engineering, 

University, Glasgow 

1865 *Rev. Francis Redford, M.A., Silloth 

1836 David Rhind, Esq., 54 Great King Street 210 
1867 *James Richardson, Esq., 16 Coates Crescent 

1859 Professor Richardson, Durham 

1818 William Richardson, Esq., Cheltenham 

1840 Martyn J. Roberts, Esq., Crickhowell, South Wales 

1859 *George Robertson, Esq., C.E., 47 Albany Street 
1832 Dr Montgomery Robertson, Mortlake, Surrey 

1860 *Dr William Robertson, 28 Albany Street 

1862 *Dr E. Ronalds, Bonnington Bank 

1852 *Alex. James Russell, Esq., C.S., 9 Shandwick Place 

1837 J. Scott Russell, Esq., 5 Westminster Chambers, Lon- 

don 220 

1859 * Robert Russell, Esq., Pilmuir, Leven, Fife 

1863 *James Sanderson, Esq., Surgeon-Major, 17 Claremont 

Crescent 

1864 *Rev. D. F. Sandford, 19 Rutland Street 

1849 *Edward Sang, Esq., 2 George Street 
1846 *Dr Schmitz, London 

1853 *Hugh Scott, Esq. of Gala, Galashiels 
1840 Sir William Scott, Bart., Ancrum 

1864 *Professor Sellar, 15 Buckingham Terrace 

1850 *Dr William Seller, 18 Northumberland Street 

1834 Dr Sharpey, Prof. Anatomy, Univ. Coll., London 230 

1844 *Sir James Y. Simpson, Bart., Prof, of Midwifery, 52 

Queen Street 
1829 Ven. Archdeacon Sinclair, Kensington 

1859 *William F. Skene, LL.D., W.S., 20 Inverleith Row 
1837 Arch. Smith, Esq., Lincoln's Inn, London 
1839 David Smith, Esq., W.S. (Treasurer), 10 Eton Terrace 

1863 *Dr John Alex. Smith, 7 West Maitland Street 

1866 *Dr John Smith, 20 Charlotte Square 
1855 *R. M. Smith, Esq., 4 Bellevue Crescent 

1846 *Professor Piazzi Smyth, 1 Hillside Crescent 

1822 Sir James South, Kensington 240 

1866 *Professor Spence, 21 Ainslie Place 

1850 *Dr James Stark, 21 Rutland Street 

1843 Henry Stephens, Esq., Red Braes Cottage, Bonnington 

1847 *Moses Steven, Esq. of Bellahouston, 12 Manor Place 



1844 *David Stevenson, Esq., C.E., 25 Royal Terrace 

1848 *Thomas Stevenson, Esq., C.E., 17 Heriot Row 

1858 *Rev. Dr Stevenson, 37 Royal Terrace 

1866 *Dr T. Grainger Stewart, 25 Queen Street 

1848 ^Patrick James Stirling, Esq., LL.D., Kippendavie House 

1823 Captain T. D. Stuart, H.M.I.S. 250 

1848 *William Swan, Esq., Professor of Natural Philosophy, 

St Andrews 

1844 * Archibald Campbell Swinton, Esq., Kimmerghame 
1830 Professor Syme, Millbank House, Canaan 

1854 Dr John Addington Symonds, Clifton, Bristol 

1861 ^Professor P. Guthrie Tait (Secretary), 6 Greenhill 
Gardens 

1846 Dr Taylor, Pau, France 

1840 Right Rev. Bishop Terrot, 9 Carlton Street 

1823 Alexander Thomson, Esq. of Banchory, Aberdeenshire 

1843 *Dr Allen Thomson, Prof. Anatomy, Univ., Glasgow 

1866 *Dr Fraser Thomson, Perth 260 
1842 James Thomson, Esq., C.E., Norfolk Square, Hyde Park, 

London 

1863 *Dr Murray Thomson, Roorkee, East Indies 

1864 *R. W. Thomson, Esq., C.E., 3 Moray Place 

1847 *Sir William Thomson, Prof. Nat. Phil., Glasgow 

1849 *William Thomas Thomson, Esq., Bonaly 

1855 *Dr Wy ville Thomson, Prof. Nat. Hist, and Geology, Belfast 
1822 Sir W. C. Trevelyan, Bart., Wallington, Morpeth 

1867 *William Turnbull, Esq., 14 Lansdowne Crescent 

1861 *Professor Turner, 7 Brunswick Street, Hillside 

1849 *Most Noble the Marquis of Tweeddale, K.T. 270 

1867 *Peter Waddell, Esq., Claremont Park, Leith 

1864 *Arthur Abney Walker, Esq., 32 Melville Street 

1829 James Walker, Esq., W.S., Tunbridge Wells 

1864 *William- Wallace, Ph. D., Glasgow 

1808 James Wardrop, Esq., London 

1853 Dr James Watson, Bath 

1866 *John K. AVatson, Esq., 14 Blackford Road 

1866 *Dr Patrick Heron Watson, 16 Charlotte Square 

1862 *Rev. Robt. Boog Watson, Madeira, 4 Bruntsfield Place, 

Edinburgh 
1840 Allan A. Maconochie Welwood, Esq. of Meadowbank 

and Pitliver. 280 

1858 *Dr Thomas Williamson, 40 Quality Street, Leith 
1834 Dr Isaac Wilson 
1847 Professor John Wilson, College 

1863 *Dr J. G. Wilson, Glasgow 

1864 *Dr Alexander Wood, 10 St Colme Street 
1864 *Dr Andrew Wood, 9 Darnaway Street 
1855 Dr Wright, Cheltenham 

1864 *Robert S. Wyld, Esq., W.S., 19 Inverleith Row 

1861 *James Young, Esq., Limefield, Mid-Calder 

1863 *Dr John Young, Professor of Natural History, Glas- 
gow 290 



Fellows elected between the commencement of the Session and the 1st January of the following year are entered under the latter 
date, by which their Subscriptions are regulated : — Thus, Fellows elected in December 1865 have the date of 1866 prefixed 
to their names. 



VOL. XXIV. PART III. 



/ 



CONTENTS. 



PART I. (1864-65.) 



II. On the Cause and Cure of Cataract. By Sir David Brewster, K.H 
F.R.S., ....... 

III. On Hemiopsy, or Half- Vision. By Sir David Brewster, K.H., F.R.S. 

IV. Miscellaneous Observations on the Blood. By John Davy, M.D 

F.R.S., Lond. and Edin., &c, .... 



PAGE 



I. On the Principle of Onomatopoeia in Language. By Professor Blackie, 1 



11 
15 

19 



V. A Study of Trilinear Co-ordinates : being a Consecutive Series of 

Seventy-two Propositions in Transversals. By the Rev. Hugh 
Martin, M.A., Free Greyfriars', Edinburgh. Communicated by 
Professor Kelland, . . . . . .37 

VI. Note on Confocal Conic Sections. By H. F. Talbot, Esq., , . 53 

VII. On the Motion of a Heavy Body along the Circumference of a Circle. 

By Edward Sang, Esq., . . . . • .59 

VIII. Experimental Inquiry into the Laws of the Conduction of Heat in Bars. 
Part II. On the Conductivity of Wrought Iron, deduced from the 
Experiments of 1851. By James D. Forbes, D.C.L., LL.D., 
F.R.S., V.P.R.S. Ed., Principal of St Salvator and St Leo- 
nard's College, St Andrews, and Corresponding Member of the 
Institute of France. (With five Plates, L-V.), . . 73 

IX. Some Observations on the Cuticle in relation to Evaporation. By John 

Davy, M.D., F.R.SS. Lond. and Edin., . . .111 

X. On the Contact of the Loops of Epicycloidal Curves. By Edward Sang, 

Esq. (With seven Plates, VI.-XIL), . . . .121 



xxiv CONTENTS. 

PAGE 

XL Researches on MalfatWs Problem. By H. F. Talbot, Esq., . 127 

XII. On the Law of Frequency of Error. By Professor Tait, . . 139 

XIII. On the Application of Hamilton's GJiaracteristic Function to Special 

Cases of Constraint. By Professor Tait, . . . 147 

XIV. On the Tertiary Coals of New Zealand. By W. Lauder Lindsay, 

M.D., F.L.S., &c, Honorary Fellow of the Philosophical Insti- 
tute of Canterbury, New Zealand, .... 167 

XV. On Variability in Human Structure, with Illustrations from the Flexor 
Muscles of the Fingers and Toes. By W.\i. Turner, M.B. (Lond.) 
F.R.S.E., Senior Demonstrator of Anatomy in the University 
of Edinburgh, ....... 175 

XVI. Examination of the Storms of Wind which occurred in Europe during 
October, November, and December 1863. By Alexander Buchan, 
M.A., Secretary to the Scottish Meteorological Society. (With 
nine Plates, X1II.-XXL), . .... 191 

XVII. On the Celtic Topography of Scotland, and the Dialectic Differences in- 
dicated by it. By W. F. Skene, Esq., .... 207 

XVIII. On the Bands formed by the Superposition of Paragenic Spectra pro- 
duced by the Grooved Surfaces of Glass and Steel. Part I. By 
Sir David Brewster, K.H., F.R.S., Lond. and Edin. (With 
a Plate, XXII.), ...... 221 

XIX. On the Bands formed by the Superposition of Paragenic Spectra pro- 
duced bij the Grooved Surfaces of Glass and Steel. Part II. By 
Sir David Brewster, K.H., F.R.S., Lond. and Edin. (With 
a Plate, XXIIL), ...... 227 



PAET II. (1865-66.) 

XX. On the Influence of the Doubly Refracting Force of Calcareous Spar 
on the Polarisation, the Intensity, and the Colour of the Light which 
it Reflects. By Sir David Brewster, K.H., F.R.S., . . 233 



CONTENTS. xxv 



PAGE 



XXI. Additional Observations on the Polarisation of the Atmosphere, 
made at St Andrews in 1841, 1842, 1843, 1844, and 1845, 
By Sir David Brewster, K.H., D.C.L., F.R.S., &c, 247 

XXII. On the Laivs of the Fertility of Women. By J. Matthews 

Duncan, M.D., ...... 287 

XXIII. On some Laws of the Sterility of Women. By J. Matthews 

Duncan, M.D., . . . . . .315 

XXIV. On a New Property of the Retina. By Sir David Brewster, 

K.H., D.C.L., F.R.S., &c, . . . .327 

XXV. On the Classification of Chemical Substances, by means of Generic 

Radicals. By Alexander Crum Brown, M.D., D.Sc, . 331 

XXVL Some Observations on Incubation. By John Davy, M.D., F.R.SS. 

Lond. and Edin., . . . . . .341 

XXVII. Report on the Hourly Meteorological Register kept at Leith Fort 
in the Years 1826 and 1827. By Sir David Brewster, 
K.H., D.C.L., F.R.S. (With two Plates, XXIV., XXV.), 351 

XXVIII. On the Buried Forests and Peat Mosses of Scotland, and the Changes 
of Climate which they Indicate. By James Geikie, Esq., of 
the Geological Survey of Great Britain. Communicated 
by Archibald Geikie, Esq., F.R.S., . . . 363 

XXIX. A Notice of Recent Measures at the Great Pyramid, and some De- 
ductions flowing therefrom. An Address delivered to the 
Royal Society, Edinburgh, at the request of the Council, 
by Professor C. Piazzi Smyth, Astronomer Royal for Scot- 
land. (With three Plates, XXVI.-XXVIII.), . . 385 

XXX. Observations on Neiv Lichens and Fungi collected in Otago, New 
Zealand. By W. Lauder Lindsay, M.D., F.L.S., Honorary 
Fellow of the Philosophical Institute of Canterbury, New 
Zealand. (With two Plates, XXIX., XXX.), . . 407 

VOL. XXIV. PART III. g 



xxvi CONTENTS. 



PAGE 



XXXI. Description of Calamoichthys, a new Genus of Ganoid Fish from 
Old Calabar, Western Africa, forming an addition to the 
Family Polypterini. By John Alexander Smith, M.D., 
F.R.C.P.E.,F.R.S.E. (With two Plates, XXXI., XXXII.), 457 

XXXII. Note on Formulae representing the Fecundity and Fertility of 

Women. By Professor Tait, ..... 481 



PART III. (1866-07.) 

XXXIII. On the Colours of the Soap-Bubble. By Sir David Brewster, 

K.H., F.R.S. (With a Plate, XXXIII.), . . .491 

XXXIV. On the Figures of Equilibrium in Liquid Films. By Sir David 

Brewster, K.H., F.R.S. (With three Plates XXXIV.- 
XXXVI. i, .505 

XXXV. On the Third Co-ordinate Branch of the Higher Calculus. By 

Edward Sang, Esq., . . . . .515 

XXXVI. On Functions with Recurring Derivatives. By Edward Sang, 

Esq., ....... 523 

XXXVII. On the Application of the Principle of Relative, or Proportional, 
Equality to International Organisation. By Professor 
Lorimer, . . . . . . .557 

XXXVIII. Some Mathematical Researches. By H. Fox Talbot, Esq., . 573 

XXXIX. On Centres, Faisceaux, and Envelopes of Homology. By Rev. Hugh 
Martin, M.A., Member of the Mathematical Society of 
London, and Examiner in Mathematics in the University 
of Edinburgh. Communicated by Professor Kelland, . 591 

XL. On the Arctic Shell- Clay of E lie and Errol, vieived in connection 
with our other Glacial and more recent Deposits. By the Rev. 
Thomas Brown, F.R.S. E. (With a Plate, XXXVIL), . 617 

XLI. Description of a Double Holophote Apparatus for Lighthouses, and 
of a Method of Introducing the Electric or other Lights. By 
Sir David Brewster, K.H., D.C.L., F.R.S. (With a 
Plate, XXXVIII.), 633 



CONTENTS. xxvii 



PAGE 



XLII. On a Lower Limit to the Poiver exerted in the Function of Partu 

rition. By J. Matthews Duncan, M.D., &c, &c, . 639 

XLIII. On the Motions and Colours upon Films of Alcohol and Volatile 
Oik, and other Fluids. By Sir David Brewster, K.H., 
F.R.S. (With a Plate, XXXIX.), . . .653 

XLIV. On the Sophists of the Fifth Century, B.C. By Professor Blackie, 657 

XLV. On the Diurnal Variation of the Magnetic Declination at Tre- 
vandrum, near the Magnetic Equator, and in both Hemispheres. 
By John Allan Broun, Esq., F.R.S. , late Director of the 
Observatory of His Highness the Maharajah of Travancore, 
G.C.S.I., at Trevandrum. (With five Plates, XL.-XLIV.) 600 

XLVI. On an Application of Mathematics to Chemistry. By Alexander 

Crum Brown, M.D., D.Sc., . . .691 

XLVI1. Description of Pygopterus Greenockii (Agassis), with Notes on 
the Structural Relations of the Genera Pygopterus, Amblyp- 
terus, and Eurynotus. By Ramsay H. Traquair, M.D., 
Demonstrator of Anatomy in the University of Edinburgh. 
Communicated by Wm. Turner, M.B. (With a Plate, 
XLV.), . 701 

XLVIII. On the Physiological Action of the Calabar Bean (Physostigma 
venenosum, Balf.) By Thomas R. Fraser, M.D., Assistant 
to the Professor of Materia Medica in the University of 
Edinburgh. Communicated by Professor Christison, M.D. 
D.C.L., V.P.R.S.E., .... 



Proceedings of Statutory General Meetings, &c, 

List of Members Elected, ...... 

List of the present Ordinary Members, in the order of their Election, . 
List of Non-Resident and Foreign Members, elected under the Old Laivs, 

„ Honorary Fellows, . ..... 

„ Fellows Deceased, Resigned, and Cancelled, from 1864 to 1867, 
Public Institutions, &c, entitled to receive the Transactions and Proceedings of 
the Society, ....... 

List of 'Donations continued from Vol. XXIII., p. 855, 
Index, ....... 



715 

789 
795 
797 
804 
804 
806 

808 
810 
831 



TEANSACTIONS. 



I. — On the Principle of Onomatopoeia in Language. By Professor Blackie. 

(Read 19th December 1864.) 

By omfiuromuu the Greek grammarians understood that principle, or tendency 
in the growth of language, according to which certain words are formed by an 
imitation of the sounds which they signify. Thus, hy%, the root of the Greek 
word oyxasSai, to bra?/, may be considered to have been formed of a human mimicry 
of that animal to which human beings of the lowest cerebral capacity are peculiarly 
compared ; and in the same way, laogh, the Gaelic for a calf, seems to contain a 
sound to which only the throats of Highland calves, Highland chieftains, and 
Highland crofters are competent. The word onomatopoeia, like some other tech- 
nical terms of the old grammarians, is not particularly happy, for it means only 
and generally word-making, or rather name-making, and says nothing of the prin- 
ciple by which the special class of words in question is made. Instead of this 
term, therefore, I should prefer to speak of the imitative or pictorial principle in 
the formation of human speech ; and I should contrast the whole class of words 
in which the operation of this principle can be traced, with another class, derived 
from ideas or notions [about the thing to be named in the mind of the word- 
maker. Thus, the modern Greeks call a cock kztwo, that is, the fowl, or flying 
animal, from airopu.!, to fly ; and the Latin word, equus, a horse, if it comes, as 
Professor Muller says, from the Sanscrit root d'su, swift, will be another word 
formed on the same principle. The roots of these words I propose to call notional 
roots, as contrasted with the onomatopcetic class of roots, which I propose to 
call pictorial roots, or roots formed by plwnic imitation. 

Professor Muller, in his valuable work on the Science of Language, has, in 
both volumes, either denied altogether the existence of this class of words, or 
treated them with such marked disfavour, that in his system they do not appear 
at all as effective agents in the formation of reasonable speech, but merely play a 
subordinate and scarcely human part in the precincts of the poultry-yard and 
the pig- sty. If, in the central table-land of Asia, before the divarication of the 
great Aryan races, a Persian pig gave a grunt, the learned Professor might perhaps 

VOL. XXIV. PART I. A 



2 PROF. BLACKIE OX THE PRINCIPLE OF ONOMATOPCEIA IN LANGUAGE. 

be willing to admit, or might be forced to admit, that there was some connection 
in the way of mimetic reproduction between the sound uttered by that animal 
and the words 7 g^« in Greek, grunnio in Latin, grunt in English, and grump>hie 
in Scotch. If, when the sacred chickens were observed by the Roman augurs in 
their cages to give forth an attenuated indication of the approaching fates, accord- 
ing to their vocal capacity, and if the speakers of the Latin dialect of the Aryan 
family agreed to designate the sound then emitted by the root pipi, familiarly 
known as a verb of the fourth conjugation, pipire, with the variety pipilare, 
applied to sparrows — in this case also, we presume, those who disown the pic- 
torial principle would be inclined to concede some pretty mimicry of the small 
unreasoning by the great reasoning animal. Or, to take an example from an 
altogether different quarter, in the word " chirumvurumvuru, used by the Africans 
on the Zambesi river, to designate a sudden violent tornado, with lightning, 
thunder, and rain, who can refuse to recognise a beautiful imitation of the 
long-continued roll of peals of thunder in a mountain district?"* But then 
they would say that in forming such words a man acts as a parrot and not as a 
man ; and in the philosophy of human speech we can take no account of an 
element which denies the distinctive character — namely, reason— of the being 
who forms it. It is against this view of the part played by the imitative principle 
of our nature in the formation of language that I now submit a few observations. 
In treating this matter, I shall first state the arguments in favour of the exten- 
sive operation of this principle, which appear to me conclusive, and then shortly 
consider the nature of the objections that have been brought against it. But, be- 
fore making a regular muster of the arguments for or against any position, it 
appears to me to be of the utmost consequence to see how the presumptions lie. 
When a man is tried before a jury for a special act of felonious appropriation, 
the fact that he is habit and repute a thief, although no part of the evidence on 
which he can be convicted, will certainly operate against him to some extent 
in the minds of the most impartial jury. In the same way, it must have been 
observed that in the discussion of the most famous literary, scientific, and philo- 
sophical questions, there is an under-current of presumption of some kind or other, 
which secretly determines which side the reasoner will take, more powerfully 
than all the arguments that are articulately brought forward, — a presumption of 
which these arguments are sometimes only the servile satellites. So, in the 
present case, I ask, first, is there any presumption why words should not be formed 
by the human voice, in imitation of certain sounds emitted by or connected with 
objects in the external world ? Man has, no doubt, been well defined a reasonable, 
or at least a reasoning animal ; but he is no less truly, and no less largely, an 
imitative animal. It may be said that there are more persons in the world who 
can give true pictures of things by word or line, than there are who can argue 

* On the Zambesi, Notes of a long Journey. By James Stewart. (Good Words, Feb. 1865.) 



PROF. BLACKIE ON THE PRINCIPLE OF ONOMATOP(EIA IN LANGUAGE. 3 

about them soundly ; for one instance of false portraiture in common conversation, 
you shall have a hundred exhibitions of bad logic. From the earliest words and 
actions of the child to the ripest productions of dramatic genius, you have the 
principle of imitation constantly and intensely at work. Many a literary repu- 
tation, exercising a powerful sway over thousands and tens of thousands of 
delighted readers, rests in a great measure on mimicry, on what may be called 
a sort of parrot work, in the service of reason, no doubt, but not at all dependent 
upon any high function of reason for its potency or its popularity. It has 
seldom been heard that the most effective mimics are the most profound reasoners ; 
and, on the other hand, a profound reasoner is often found deficient in that vivid 
power of imitating the striking points of detail which is the strength of the 
popular novelist, and the best spice of convivial conversation. There is therefore 
no presumption against the action of this so universal principle in the formation 
of language, but rather the contrary. And if the element by which sounds in the 
external world are signified in human speech is itself sound, how should we 
more naturally expect the one to express the other, than by some sort of imita- 
tion, more or less complete, according to the character of the vocal organ? I go, 
then, to nature, prepared to expect imitative phenomena in human speech ; and I 
find them, not one here and one there, but everywhere in the richest abundance. 
Can any one hear the English words smash, dash, thump, dumb, squeak, creep, 
clatter, chatter, click-clack, ding-dong, sigh, sob, moan, groan, hurry -skurry, skimble- 
skamble, wiggle-waggle, and not believe that these words were framed by the 
human voice, with the express intention, more or less successfully realised, of 
giving a dramatic representation of the thing signified ? This is so obvious, that, 
as already stated, Professor Muller has been forced to admit it, to a certain 
extent; but, at the same time, watches with the sternest jealousy that the action 
of such a principle shall not be allowed to travel beyond the narrow precincts of 
the poultry-yard and the pig-sty. But, however he may wish to circumscribe 
the operation of the principle, it is quite certain that it acts not only most 
powerfully in the low region here indicated, but that this pictorial power of words 
is one of the most powerful instruments by which human speech is made to affect 
the human imagination, and becomes an instrument in the skilful wielding of 
which one of the great merits of a great poet has always been felt to consist. 
When, for instance, Homer says : — 

Aovirriffev rs ffiauv agaCSjtrs b% rsu^icc sir avrSJ. 
" With a hollow sound he smote the ground, and his armour rattled o'er him ;" 

or Go'the — 

" Aus dem hohlen dunklen Thor 
Drdngt sich cin buntes Gewimmel hervor^ 

every one feels that the poet, under the influence of the rhythmical instinct 
which is an expression of reason, is only using the materials of language for 






4 PROF. BLACKIE ON THE PRINCIPLE OF ONOMATOPCEIA IN LANGUAGE. 

producing an sesthetical effect, on the same imitative principle by which these 
materials themselves were originally framed. And we can prove the actual 
making of words on this principle from observation. A happy father calls his 
child "little goo-goo /" Why? Because the little creasy-armed, chubby-faced 
Hopeful has a throat, and g is a guttural letter ; and, therefore, as naturally as a 
chicken cries pip, pip, the baby sends forth goo, goo, as the first notice of its 
march into the realm of articulate speech ; and the delighted parent, by the 
exercise of the parrot faculty, immediately forms a name for his son, which 
might have remained for ever, as the only name it should get, did not the con- 
ventional rights of baptism interfere, not to mention the long prescriptive claim 
in favour of baby and boy, which the labial letters from old Greek and Roman 
days have succeeded in establishing against the guttural. For I certainly do 
believe, whatever may be said to the contraiw, that the Hebrew word em, the 
Greek pata and wnig, the German Amme, and the common English ma\pa\ and 
baby, have something to do with the use of the labial letters, so natural to the 
toothless gums of children, and so obvious in the cries of certain animals. Of the 
consonants indeed, which brutes use to modify their vocal cries, of which the 
vowel is always the grand clement, the labials and gutturals, along with the 
snarling R, the rolling L, and the sibilant S, seem to be the most common. We 
shall not therefore be surprised to find an ox called Bo in Latin, Greek, and Gaelic, 
or to hear the bellow of oxen called //,yxa<r3a/ in Greek, while the bleat of sheep is 
called Mxuedui, and the cry of goats, in German meckern, for which I do not know 
that we have a specific word in English. And if the Greeks say i/>.«x™ for the 
bark of a dog, it is not because their language is not mimetic in this case, while 
ours certainly is, but because i-?.«x™ is merely a lengthened derivative form of the 
root 6x, Avhich is only a feebler form of our English lionl, German heulen. In the 
same way that the letter R in the Greek -/.^mr,, the Latin corvus, the Hebrew 21V, 
and the English crow, has something to do with the sound uttered by that class 
of animals, I shall continue to believe, without any reference to Grimm's Law, 
so long as in the world of animated sound neither swallows shall have been 
heard to grunt on the eaves, nor pigs to twitter in the st} 7 , nor bulls to mew in 
Bashan, nor cats to bellow at the fireside. 

Let so much therefore be allowed,— be held as admitted, — though not without 
manifest unwillingness by those who disown the principle we now advocate. But 
now comes the more important question, for the sake of which alone the preceding 
examples have been given, as a sort of postulate, rather than as demanding proof. 
Is this all ? If only a few names of animals, and certain phenomena in nature 
always accompanied by sound, are to be explained by the principle of pictured 
articulation, we are advanced but a very short way, and the great body of 
the roots of a language, expressing not sounds but notions, remains unexplained. 
When I express the idea of thinking in Latin by the root med, in Greek by ^r, 



PROF. BLACKIE ON THE PRINCIPLE OF ONOMATOPOEIA IN LANGUAGE. 5 

and in English by think, what possible connection can such words have with 
screaming, or grunting, or twittering, or with the cry of any unreasoning animal ? 
For man, as a reasoning animal, must have a method of proceeding in forming 
his language, altogether different from the procedure which would suffice for 
unreasoning brutes ; his discourse is not only p»«j, mere voice, but it is \6yog, that 
is simply the outside of reason, and expressed in Greek (as all the world knows) 
by the word which likewise signifies reason. Depend upon it, all the important 
roots of a language must be notional ; otherwise, we suppose man acting without 
reason, and our philosophy sinks into the lowest sensationalism of the French 
school of the last century. 

Now, before answering this argument, I must again protest distinctly against 
the presumption here implied, that the assertion that we do any thing without 
the intervention of conscious notions and ideas is degrading to man, and ignores 
that reason which is his characteristic. We eat, drink, sleep, love, hate, dance, 
fly into sublime passions, and write lofty poetry, not without reason, indeed, but 
certainly in nowise by virtue of consciously worked out products of reason, 
called abstract ideas. If it should be found, therefore, that certain words denot- 
ing mental action are only a secondary application of words originally painting 
an outward mechanical action or position, or even a mere sound, I see nothing to 
be ashamed of in the matter. A man may make himself a pig, or worse than a 
pig in many ways, but certainly not merely by painting a pig-sty, or by ven- 
triloquizing a grunt, or even by borrowing a grunt, for the expression of some 
moral or metaphysical idea. The degradation to a reasonable being in the matter 
of language consists, not in the borrowing from physical sources, but in not sub- 
mitting the borrowed physical material to a native metaphysical treatment. 

This premised, we remark that it is a known tendency of language to grow, not 
by the creation of new roots, when they are not necessary, but by a dexterous use 
of the stock already acquired. In harmony with this fact, we have a right to sup- 
pose that the original framers of language having succeeded, by the principle of 
phonic imitation, in making a vocabulary to express the sounds made by animals 
or sounding bodies, and the related names by which these should be known, would 
not stop here, but would proceed to apply the same principle to a much wider and 
more important range of ideas. Nor was the stepping-stone far to seek, by which 
they soon learned to pass from the domain of single imitated sounds to the domain 
of actions generally, and of all sorts of ideas. For if we attend to the process of 
nature in such cases, we shall observe three facts which would necessarily help 
to work out the original stock of strictly pictorial words imitating mere sounds, 
to a large class of words, including all the most important verbs which language 
in its early stages required. The first of these facts is, that most actions which 
attract the notice of men are, in the first place, accompanied by certain sounds 
or noises, which serve to indicate the approach, and to express the manner and 

VOL. XXIV. PART I. B 



6 PROF. BLACKIE ON THE PRINCIPLE OF ONOMATOPOEIA IN LANGUAGE. 

intensity of their energy. The second fact is, that between sounds and certain 
feelings and ideas, not accompanied by any sound, there are certain strong analo- 
gies, such as that which the blind man indicated, when he said that he thought 
scarlet colour was like the sound of a trumpet ; and these analogies, taken advan- 
tage of by the dexterous and economic framers of language, would necessarily 
lead to the designation of a number of ideas expressive of noiseless vision or 
touch, by words possessing some vocal and audible analogy. The third fact is, 
that all external impressions made upon our senses, which, if not the cause, are 
certainly one of the necessary factors of all human knowledge, are never expressed 
without the production of certain pleasant or unpleasant feelings, and certain 
affection of the nervous system, on which the utterance of articulate sound de- 
pends ; and as effects always correspond to causes, it cannot but be that the vocal 
utterance from within educed by any strong impression from without, shall in 
some way or other represent the character of the source from which it sprang. 
Let us examine these three facts separately, and see to what classes of results 
in the formation of language they unavoidably lead. Take the word Kill to be- 
gin with. You ask what connection is there between the sound of this word and 
the action signified ? I reply, that I do not know, because there are many 
words in all languages, derivative both in meaning and form, whose original type 
is not now recoverable ; but there is another English word, slay, signifying the 
same thing, the original form of which is the German word, schlagen, to strike, 
and here I distinctly see a phonic congruity between the rough action signified, 
and the rough word Schlag, by which it is expressed. The act of striking is 
generally accompanied by a hard, sharp noise; and so, hard, sharp syllables, 
as in the English words, knock, rap, are used to express that act. Or take the 
Sanscrit root mar, of which Muller has made so much, and who does not see 
that it expresses something rude and harsh, as much as the English word crush, 
and the French word ecraser? In the same way the root ar, signifying to 
plough, and which appears in the Hebrew pN the earth, as well as in the Greek 
adverb %«£*, is evidently a phonetic expression of the rough sound of earth or 
gravel when stirred, containing a combination of letters which, when inverted, 
appears in gravel, grain, yt>u<pu, scratch, -xucdeeu. 

In the same way, actions accompanied by slender soft sounds are expressed by 
weak vowels, as to creep, to sneak, and to slink. Is it not also plain, that 
whether we take the Greek xxiima or the English steal, we find that these words 
are so formed as to present a dramatic contrast to d^dfy and rob, which signify 
the same kind of abstraction, accompanied with violence and noise ? And if you 
say that the Latin fur does not express anything of this kind, I thank you for the 
observation, and reply that the Greek verb p«^«, from which fur is derived, does 
not originally imply the silent stealthiness of felonious appropriation, but rather 
the sudden, rude act, by which a thief is apprehended. Contrast with these 



PROF. BLACKIE ON THE PRINCIPLE OF ONOMATOPOEIA IN LANGUAGE. 7 

words the English word tumble, and you will observe that the awkward, clumsy, 
hollow roll with which the act of accidental falling is generally accompanied, finds 
expression here to such a degree that the words to tumble and to stand seem as 
much opposed to one another as a round rowley-powley pudding is to the sharp, 
thin, clear knife which cuts it. And this brings me to my second great fact, — 
Why has the word k?iife a k in it? Why the Gaelic sgian, why the Latin cutter? 
Is this altogether accidental ? Certainly not. K is a sharp letter, perhaps the 
sharpest in the alphabet, and therefore in all languages appears in words which 
signify sharpness, as in the Latin word acies, Greek ax^s, Sanscrit krit, to cut, 
with the Latin ccedo, and probably the Gaelic cath, a battle. The Greek xoV™ 
contains the same initial letter, although from the intrusion of the labial it it 
is a less perfect word to express a clean, sharp stroke than the simple dental 
which appears in the other roots. For the labials, being uttered by rounded, un- 
pointed organs, are naturally used to express bluntness, as the very word blunt, 
Greek a^exij, plainly proves. Hollow vowels and hard consonants will in all 
cases be applied to express the reverse of what is sharp and thin. So tundo in 
Latin is to beat, not sharply, like our word rap, but broadly and bluntly, as with 
a mallet. Hence obtundere aures, to bore a person with talking, to be constantly 
beating, and thumping, and drumming your crotchets upon the tympanum of his 
ear. So, when a man's intellect is not very sharp, he is said to be muddled or 
fuddled; and if muddled is only a verbal form of mud, you will easily under- 
stand that something soft, broad, round, not at all clear, and not very stable, is 
understood by the verb as well as by the noun. We thus see how not only sound, 
but everything perceptible to vision or to touch — that is to say, the whole range 
of phenomenal knowledge — comes under the derided principle of dvo^aro^oiia ; and if 
there can be any stronger proof given of the unlimited range of articulate sound, 
in mimetically expressing things which have nothing to do with sound, the 
English word mum, for silence, contains that proof. M is the labial which most 
completely closes the lips, and sends the breath up through the nose ; hence it 
appears in the Latin mutus, the Greek tivu for closing or shutting, not the mouth, 
but the eyes, and in the English dumb, which in German is dumm, stupid, be- 
cause stupid people have often the sense to sit silent in company, and thus not 
betray their stupidity. I conclude these illustrations of the second of the three 
great facts by a remark on the word stand, previously used. This word, which is 
a bastard present, formed from the old past tense, like the Alexandrian Greek 
eriw, has for its root the Sanscrit sthd, in Latin stare. Now, any one may see that 
this word stands more firmly on its legs than the word timible, with which we 
contrasted it. Why is this ? There is no firmness or decision in any part of this 
word, just as in the cognate word mumble there is a plain want of determinative 
emphasis in the conglomeration of the letters. But when I say sta, I bring my 
teeth together with a decision which shows that I am suiting the word to the 



8 PROF. BLACKIE ON THE PRINCIPLE OF OXOMATOPCEIA IN LANGUAGE. 

action, and that the firmness which I exhibit in the muscles of my legs is not to 
be accompanied with any looseness in the action of my jaws. And that this is 
not a mere fancy will be obvious to any one who considers the wide application 
which this combination of letters enjoys in words expressive of strength and deci- 
sion in all languages. Thus in English, stop, strength, strike, stride, sturdy, start ; 
in Greek, art>ayyu, tfrgspw, tfrgjjMis, argvpvos, gTiiZu, most of which have their Latin repre- 
sentatives, as stringo, strenuus, stipo. So in German, starr, streng, stossig ; and 
many others. There remains now, to complete the pictorial process by which 
language is formed, the third fact mentioned above — according to which all ex- 
ternal expressions necessarily affect in a certain way the whole nervous system 
and mental economy, and through the motion in the vital spirits thereby produced, 
modify in a corresponding way the articulation of human speech. Here we 
have a different principle altogether, as it would appear at first sight, from mere 
ovopurovroiia ; for to imitate an internal sound, and to express an internal feeling, 
seem not only different, but quite contrary actions. Nevertheless, they are in 
their effects, as in their origin, substantially one ; and Professor Muller has 
accordingly put what he calls the Poon ! pooh ! theory as much under his ban as 
the Bow-wow ! For the fact of the matter is, that an interjection, such as ah ! or 
oifiu, or eheu, and all such vocal expressions of pleasure or pain, must, by the laws 
of vitality, exhibit a certain correspondence with the sensations of which they are 
the expression. Thus any oppressive, heavy feeling in the chest will naturally 
cause a slow, protracted, dull flow of breath to proceed from the throat. The 
vowels a and «, the diphthongs aiandoi, are exactly such a flow of breath. Hence 
the interjections u, «/, 01, amplified into the verbs w^w, *«££«, h^Zp. 

There is here, therefore, a sort of natural drama enacted — a correspondence of 
the within and without — which springs fundamentally out of the same root as the 
ovofiaroKoila proper. When Aristotle called all poetry mimetic, he probably meant 
something of this kind ; for while dramatic poetry only is strictly imitative of 
outward objects, lyric poetry is dramatically expressive of inward feelings ; and 
to this the Bow-wow and the Pooh ! pooh ! departments of early word-making 
plainly correspond. 

If we now inquire what the objections are that are brought against these facts, 
indicative of the operation of the pictorial principle in the world of vocal utterance, 
we find that they require no very laboured refutation, but resolve themselves into a 
few misunderstandings and prejudices, which a single touch can brush aside. In 
the first place, if it ever was asserted by any writer that all the presently existing 
roots in any language are onomatopcetic, and that all current words are to be 
explained on this principle alone, with such assertion I have nothing to do. I 
only maintain that the original stock of which language was made up consisted 
of such roots, and that a great proportion of them, after the changes of thousands 
of years, bear their origin distinctly on their face. I do not say, however, that 



PROF. BLACKIE ON THE PRINCIPLE OF ONOMATOP(EIA IN LANGUAGE. 9 

all the words now existing in a language are to be dealt with on the supposition 
that they contain some pictorial element of the original phonic drama of human 
speech. Syllables are like sixpences, and are apt to be rubbed down in the course 
of time, till their original image and superscription can no more be traced. 

Besides, as in the Greek language the word <kdi\p6s, signifying uterinus, or born 
of the same womb, took the place of <pg<Lrug, which no doubt originally was used as 
frater in Latin, bhrdtri in Sanscrit, and brother in English, so many of the oldest 
dramatically significant roots of language may have been replaced by secondary 
roots, in which the real character that belonged to the first pictorial roots is 
lost. I do not therefore deny that equus may come from the root d'su, swift, and a 
horse signify the swift animal. Though I have no doubt that bo, an ox, is merely 
a human imitation of the bovine sound, I by no means insist that all animals 
should have received their names from the cries which they make. I only say 
that, in the original formation of language, this was one of the simplest and most 
obvious methods of designation, and a method that extended a great deal further 
than superficial observation might lead the modern speculator to believe. 

As little can I see why Professor Muller should feel it his duty to declare war 
wholesale against onomatopoeia in language, because on this or the other occasion 
some men have handled it wildly, and ridden rough-shod with it over Grimm's 
law, and the whole body of ascertained facts with regard to phonic transmigra- 
tions and transmutations. A man may talk ingenious nonsense on any branch 
of philological science with the utmost ease, in the teeth of Grimm's law, or even 
with the help of it ; but that great principle of interlingual change has nothing to 
do with the question how roots, variable according to certain laws of phonic 
change, were originally formed. The Sanscrit pitri may become the English 
father, and the Scotch fader, without touching the question whether PA and 
MA have anything to do with imitation by parents of the first untutored labial 
utterances of a child. Finally, I must be allowed to express my conviction that 
the opposition to onomatopoeia seems to arise in the minds of some speculators 
partly from a certain horror of a sort of merely animal element in the creation of 
language, which in ancient times had found acceptance with the low sensuous 
philosophy of Epicurus,* and partly, so far as the Germans are concerned, 
from a certain instinct in them which leads them to prefer what is remote to 
what is obvious, what is conceptional to what is sensational, what is fanciful to 
what is real, what is mystical to what is plain. If they blame us, not unjustly 
altogether, for having no ideas in our scholarship, we may with equal reason 
retort that they have too many, and use them often with a wild ingenuity, rather 
than with a sober discretion. If we do not make such brilliant discoveries as 
they do beyond the flaming walls of the universe, we do not, on the other hand, 

* Muller, vol. ii. p. 87, quotes a passage of Proclus from Epicurus as having suggested his 
soubriquet of the Bow-wow theory. 

VOL. XXIV. PART I. C 



10 PROF. BLACKIE ON THE PRINCIPLE OF ONOMATOPCEIA IN LANGUAGE. 

so often fail to see what directly lies before us. The same national habit of 
thought which led Forchhammer to find in the Iliad a geological account of the 
struggle betwixt land and water in the Troad, and leads Professor Muller to 
discover in the same great historic tradition a mythological fight between light 
and darkness, seems to determine the position of this distinguished philologer 
in reference to the original formation and growth of roots in language. How 
they were formed he nowhere tells us ; he does not pretend to know ; but of one 
thing he feels assured, that there is more of mystery in the matter than the easy 
mimicry of natural sounds can explain. " Are not Abana and Pharpar rivers of 
Damascus? may I not wash in them and be clean?" He will have nothing to do 
with word-painting, because it is too simple a process, seems to deal with facts 
rather than with ideas, and is not at all nrysterious. For my own part, I think 
all is mysterious with language in one sense, nothing in another. It is as natural 
for men to speak, as for birds to sing, and fountains to flow ; and that when 
they did speak, they spoke originally from imitation of natural sounds, and a 
cunning adaptation of the expressive power of the audible element, not only to 
things audible, but also to things visible and tangible, I shall continue to believe 
till some principle shall be propounded that may explain all known facts in a 
manner equally obvious and satisfactory. 

I have only to say in conclusion, that my faith in imitation as the great 
principle in the formation of the original stock of human speech, is not in any 
degree affected by the vexed question whether man was originally created full- 
grown or a baby, whether he made language for himself, or got it, as some think 
there is a peculiar piety in imagining, ready-made from the Deity. I do not 
believe that Adam got language ready-made from his Creator, for the very plain 
reason that we get nothing ready-made from the Creator, but we make it our- 
selves after a fashion, by the indwelling power of His infinite virtue and grace, 
who is never far from the meanest of His creatures. But even if the Supreme Being 
did make a present to our primal sire of a ready-made language (though I think 
this contrary to the words of Moses in Genesis ii. 19), still the fact remains 
that the grand vocal organism so presented, bears on its front the most evident 
marks of an onomatopcetic or imitative construction. Those, therefore, who hold 
that God made human language must maintain that He made it on the same 
principle on which I maintain that man made it ; for the facts are undeniable ; 
and surely it cannot be more pious to suppose that the Father of all men coined 
words for the use of His reasonable children in a manner altogether arbitrary, 
rather than on the principle of a reasonable congruity, and a beautiful adaptation. 



( 11 ) 



II. — On the Cause and Cure of Cataract. By Sir David Brewster, K.H., F.R.S. 

(Read 16th January 1865.) 

My attention was called to the subject of Cataract, in consequence of having, 
about forty years ago, experienced an incipient attack of that complaint, and 
studied its progress and cure. 

While engaged in a game at chess with Sir James Hall, who was a very slow 
player, I amused myself in the intervals with looking at the streams of light 
which radiated from the flame of a candle in certain positions of the eyelids. In 
one of these observations I was surprised by a new phenomenon, of which I did 
not immediately see the cause. The flame of the candle was surrounded with 
lines of light, of an imperfectly triangular form, some parts of which were deeply 
tinged with the prismatic colours. Upon going home from the chess club, this 
optical figure was seen more distinctly round the moon, and of course it appeared, 
with more or less brightness, round every source of light. 

Having been engaged in examining the structure of the crystalline lens in 
animals of all kinds, I soon discovered the cause of the phenomenon which I have 
described. The laminae of the crystalline lens had separated near its centre, and 
the separation had extended considerably towards its margin. The albuminous 
fluid, the liquor Morgagni, which so wonderfully unites into one transparent 
body, as pure as a drop of water, the mass of toothed fibres which compose the 
crystalline lens, had not been sufficiently supplied, and if this process of desicca- 
tion had continued, the whole laminae of the lens would have separated, and 
that state of white opacity induced, which no attempt has ever been made to 
remove. 

The continuance of this affection of the lens was naturally a subject of much 
anxiety, and I never entertained the slightest hope of a cure. My medical 
friends recommended the use of what were then called Eye Pills, but having 
received no benefit from them, and having learned from experience the sympathy 
between the eye and the stomach, I used every day, and copiously, the Pulvis 
salinus compositus, and at the end of about eight months, when playing at chess 
in the same apartment, I had the happiness of seeing the laminaa of the lens 
suddenly brought into optical contact, and the entire disappearance of the lumi- 
nous and coloured apparition with which I had been so long haunted. 

In speculating on the process by which the crystalline lens is supplied with 
the necessary quantity of fluid, it occurred to me that it might be derived from 
the aqueous humour, and that cataract might be produced when there was too 
little water and too much albumen in the fluid which filled the aqueous chamber. 

VOL. XXIV. PART I. D 



12 SIR DAVID BREWSTER ON THE CAUSE AND CURE OF CATARACT. 

Upon this hypothesis, incipient cataract might be cured in two ways : — 

1st, By discharging a portion of the aqueous humour, in the hope that the 
fresh secretion, by which the loss is repaired, may contain less albumen, and 
counteract the desiccation of the lens. 

2d, By injecting distilled water into the aqueous chamber, to supply the 
quantity of humour discharged from it. 

The first of these methods I knew to be practicable and safe, from the fact 
that a surgeon in the Manchester Infirmary, many years ago, tapped the aqueous 
chamber of a female patient forty times, in the vain hope of curing a case of 
conical cornea, which he attributed to an excess of aqueous humour. The frequent 
repetition of this operation shows how rapidly the humour is secreted, and how 
reasonable it is to suppose that, in the case of cataract,~a healthier secretion 
might be produced under medical treatment. 

Although the second method of injecting distilled water into the aqueous 
chamber presents greater difficulties, yet they do not appear to be insuperable. 
In 1827, when I happened to be in Dublin, I mentioned this method to the cele- 
brated comparative anatomist, Dr Macartney, who considered it quite practicable. 
He mentioned to me that a foreign oculist, whose name I forget, had actually 
injected distilled water into the eye of a patient with the view of supplying the 
aqueous humour that was lost during the extraction of the lens. 

My attention was recalled to these suggestions for treating incipient cataract, 
by the results of a series of experiments on the changes which take place in the 
crystalline lenses of the sheep, the cow, and the horse, after death. In these 
experiments, which were published in the Philosophical Transactions for 1837, 
the lenses were placed in a glass trough of distilled water, and exposed to 
polarised light ; and the changes thus produced were indicated by variations in the 
number and character of the polarised rings, and more palpably by the gradual 
enlargement of the lens. The distilled water passed through the elastic capsule 
of the lens. The lens increased in size daily, and at the end of several days the 
capsule burst, leaving the lens in a disorganised state, the outer laminae being 
reduced to an albuminous pulp by the water admitted through the capsule. 

These experiments have an obvious importance in reference to the cause and 
cure of the two kinds of cataract to which the human eye is subject. The aque- 
ous humour is in immediate contact with the capsule of the crystalline lens. 
When the humour, therefore, contains too little water, the lens has not a sufficient 
supply of the fluid which keeps its fibres and laminae in optical contact, and 
hence the laminae separate, and the lens becomes opaque and hard. When, on 
the contrary, the aqueous humour contains too much Avater, the capsule intro- 
duces the excess into the lens, and produces the more dangerous affection of soft 
cataract, in which it is difficult either to depress or extract the lens. 

In order to cure the first of these kinds of cataract, we must discharge a 



SIR DAVID BREWSTER ON THE CAUSE AND CURE OF CATARACT. 13 

portion of the aqueous humour, and either supply its place by injecting distilled 
water, or leave it to nature to supply a more healthy secretion. In order to cure 
the second kind, we must supply the place of the discharged humour with a solu- 
tion of albumen ; or, as in the first case, leave to nature the production of a more 
albuminous secretion. 

These views have received a remarkable confirmation from recent experi- 
ments on the artificial production and removal of cataract in the eyes of animals. 
Dr Kind, a German physiologist, whom I met at Nice in 1857, informed me that 
he had produced cataract in guinea-pigs, by feeding them with much salt, and that 
the cataract disappeared when there was no salt in their food. More recently, 
Dr Mitchell,* an American physician, produced cataract by injecting syrup into 
the subcutilar sacs of frogs ; and Dr Richardson f did the same by injecting 
syrup into the aqueous chamber of the recently dead eye of a sheep. In the ex- 
periment of Dr Mitchell, the cataract was removed from the living eye of the 
frog by surrounding the animal with water ; and in that of Dr Richardson, the 
cataract was removed from the dead eye of the sheep by replacing the syrup with 
distilled water. 

Neither Dr Mitchell nor Dr Richardson seem to have been acquainted with 
my experiments on the changes in the lens after death, published in 1837, and 
with the theory of the cause and cure of cataract there referred to ; nor with the 
distinct statement of it published in 1836, ^ and twenty years later, in 1856.§ 
Dr Rtchardson, however, has borne ample testimony to its practicability and 
safety, when he suggests, almost in my own words, " that it would be worth 
while, in the earliest stage of cataract in the human subject, to let out the aqueous 
humour, and to refill the chamber with simple water." And he has borne a 
still stronger testimony to its value by congratulating " Dr Mitchell in having 
been the earliest experimentalist to elucidate the synthesis of cataract, and to 
take the first steps towards a rational interpretation of the disease." 

The tendency of the human crystalline lens to indurate or soften, by a defect 
or excess of water in the aqueous humour, may occur at any period of life, and 
may arise from the general state of health of the patient ; but it is most likely to 
occur at that age, between 40 and 60, and often much earlier, when the lens 
experiences that change in its condition which requires the aid of spectacles. 
This change commences at one part of the margin of the lens, where its density 
is either increased or diminished. Its action in forming a picture on the retina 
thus becomes unsymmetrical, and vision is sensibly impaired. But when the 
change has taken place round the margin of the lens, its symmetrical action is 

* American Journal of tlie Medical Sciences. January 1860. 

f Medical Times and Gazette. March 31, 1860. 

| Report of the British Association, 1836, p. Ill ; and 1837, p. 12. 

§ North British Review, vol. xx. p. 167. November 1856. 



14 SIR DAVID BREWSTER ON THE CAUSE AND CURE OF CATARACT. 

restored, and by the use of spectacles the vision becomes as perfect as it was 
before the change. If glasses are not used when the change is completed, the 
eye must either strain itself, or use a strong light, to produce distinct vision in 
reading the small type and the imperfect printing which characterises the daily 
press ; and by both these processes it will, in a greater or less degree, be injured. 
It is a strange delusion, arising either from ignorance or vanity, which induces 
most people to put off the use of spectacles as long as possible. From the instant 
they are required, spectacles of different focal lengths ought to be used for the 
different purposes for which distinct vision is required, and the eyes should never 
do any work, unless they can do it with perfect distinctness and satisfaction. 
There is no branch of the healing art where science comes so directly and imme- 
diately to the relief of impaired functions as that which relates to vision, and none 
where science has been so imperfectly applied. When the change in question 
takes place, the eye requires to be carefully watched, and used with the greatest 
caution ; and if there is any appearance of a separation of the fibres or lamina?, 
those means should be adopted which, by improving the general health, are most 
likely to restore the aqueous humour to its usual state. Nothing is more easy 
than to determine the condition of the crystalline lens ; and by the examination 
of a small luminous object placed at a distance, and the interposition of small 
apertures, and small opaque bodies of a spherical form, we can ascertain the 
exact point in the lens where the fibres and laminae have begun to separate, 
and may observe from day to day whether the disease is gaining ground or dis- 
appearing. 

[Since the preceding paper was read I have seen a remarkable work, entitled 
"Etudes Cliniques sur V evacuation de VHumeuv Aqueuse dans les Maladies de 
VCEil" par Casimir Spirino, Turin, 1862. Pp. 500. M. Spirixo had, in the 
course of little more than a year, operated upon forty-five cases of cataract. In 
many of these the cataract was perfectly cured, and in others the sight was 
improved. The first case was that of a lady of eighty-one, who had cataract in 
both eyes. After thirty-two evacuations of the aqueous humour by the same 
aperture, and almost always two or three times at the same sitting, both cataracts 
disappeared, the lady was able to read, without glasses, Nos. 3 and 4 of Jaeger's 
scale, at the distance of 4 or 5 inches, and even to thread a small needle.] 



( 15 ) 



III. — On Hemiopsy, or Half- Vision. By Sir David Brewster, K.H., F.R.S. 

(Read 20th February 1865.) 

The affection of Half-vision, or Half-blindness as it has been called, was first 
distinctly described by Dr Wollaston, in a paper " On Semidecussation of the 
Optic Nerves, 1 ' published in the Philosophical Transactions for 1824. " It is now 
more than twenty years," he says, " since I was first affected with this peculiar 
state of vision, in consequence of violent exercise I had taken for two or three 
hours before. I suddenly found that I could see but half the face of a man whom 
I met, and it was the same with every object I looked at. In attempting to read 
the name Johnson over a door, I saw only son, the commencement of the name 
being wholly obliterated from my view. In this instance, the loss of sight was 
towards my left, and was the same, whether I looked with my right eye or 
my left. This blindness was not so complete as to amount to absolute black- 
ness, but was a shaded darkness, without definite outline. The complaint 
lasted only about a quarter of an hour." In 1822, Dr Wollaston had another 
attack of hemiopsy, with this difference, that the blindness was to the right of 
the centre of vision, and he has referred to three other cases among his friends ; 
but in these, the affection was accompanied with headache and indigestion. 

In republishing Dr Wollaston's paper in the "Annates de Chimieet Physique"* 
M. Arago says, that he knows four cases of hemiopsy, and that he himself had 
experienced three attacks of it, followed by headache above the right eye. 

In the " Cyclopaedia of Practical Surgery," published in 1841, Mr Tyrrell 
describes Hemiopsy as " Functional amaurosis from general disturbance." He 
informs us that " he has experienced this form of amaurosis several times," and 
that he has been consulted by several fellow-sufferers of both sexes. In all these 
cases the affection was attended with severe headache, giddiness, and gastric irri- 
tation, sometimes preceding, and sometimes following, the attack. 

In the accounts which have been given of these different cases of hemiopsy, 
no attempt has been made to ascertain the optical condition of the eye when it is 
said to be half-blind, or to determine the locality and immediate cause of the 
complaint. Dr Wollaston describes the blindness as a shaded darkness without 
definite outline. M. Arago says nothing about darkness ; and the insensibility of 
the retina, of which he speaks, must mean its insensibility to visual and not to 
luminous impressions. Mr Tyrrell, on the other hand, simply states, that the 

* 1824, vol. xxvii. p. 109. 
VOL. XXIV. PART I. E 



16 SIR DAVID BREWSTER ON HEMIOPSY, OR HALF-VISION. 

obscurity takes place in different portions of the retina, and varies in its extent at 
different times. 

Having myself experienced several attacks of hemiopsy, I have been enabled 
to ascertain the optical condition of the retina when under its influence, and to 
determine the extent of the affection, and its immediate cause. 

In reading the different cases of hemiops}-, we are led to infer that there is 
vision in one-half of the retina, and blindness in the other. But this is not the 
case. The blindness, or insensibility to distinct impressions, exists chiefly in a 
small portion of the retina to the right or left hand of the foramen cent rale, and 
extends itself irregularly to other parts of the retina on the same side, in the 
neighbourhood of which the vision is uninjured. In some cases the upper half of 
the object is invisible, the part of the retina paralysed being a little below the 
foramen centrale. On some occasions, in absolute darkness, when a faint glow of 
light was produced by some uniform pressure upon the whole of the retina, I 
have observed a great number of black spots, corresponding to parts of the retina 
upon which no pressure was exerted. 

In the case of ordinary hemiopsy, as observed by myself, there is neither dark- 
ness nor obscurity, the portion of the paper from which the letters disappear 
being as bright as those upon which they are seen. Now, this is a remarkable 
condition of the retina. While it is sensible to luminous impressions, it is in- 
sensible to the lines and shades of the pictures which it receives of external 
objects ; or, in other words, the retina is in certain parts of it in such a state that 
the light which falls upon it is irradiated, or passes into the dark lines or shades 
of the pictures upon it, and obliterates them. This irradiation exists to a small 
degree, even when the vision is perfect at the foramen centrale, and it may be 
produced artificially in a sound eye, on parts of the retina remote from the fora- 
men, and as completely, though temporarily, as in hemiopsy. In order to prove 
this, we have only to look obliquely at a narrow strip of paper placed upon 
a green cloth, that is, to fix the eye upon a point a little distant from the 
strip of paper. After a short time the strip of paper will disappear partially or 
wholly, and the space which it occupied will be green, or the colour of the ground 
upon which it is laid.* 

This temporary insensibility of the retina in the part of it covered by the 
picture of the strip of paper, or its inability to maintain constant vision of it, can 
arise only from its being paralysed by the continued action of light, an effect not 
likely to be produced, and never observed, in the ordinary use of the eye. 

The insensibility of the retina, in cases of hemiopsy, and the consequent irra- 
diation of the light into the space occupied with the letters, or the objects which 
disappear, though a phenomenon of the same kind as that which takes place in 

* Letters on Natural Magic. Let. II. p. 13. 



SIR DAVID BREWSTER ON HEMIOPSY, OR HALE-VISION. 17 

oblique vision, has yet a very different origin. The parts which are in these cases 
affected extend irregularly from the foramen centrale to the margin of the retina, 
as if they were related to the distribution of its blood-vessels, and hence it was 
probable that the paralysis of the corresponding parts of the retina was produced 
by their pressure. This opinion might have long remained a reasonable expla- 
nation of hemiopsy, had not a phenomenon presented itself to me, which places it 
beyond a doubt. When I had a rather severe attack, which never took place 
unless I had been reading for a long time the small print of the Times newspaper, 
and which was never accompanied either with headache or gastric irritation, I 
went accidentally into a dark room, when I was surprised to observe that all the 
parts of the retina which were affected were slightly luminous, an effect invari- 
ably produced by pressure upon that membrane. If these views be correct, 
hemiopsy cannot be regarded as a case of amaurosis, or in any way connected, 
as has been supposed, with cerebral disturbance. 

Dr Wollaston endeavoured to explain the phenomena of hemiopsy, and the 
fact of single vision with two eyes, by what he calls the semidecussation of the 
optic nerves, a doctrine which Sir Isaac Newton had suggested, and employed to 
account for single vision* A fibre of the right-hand side of the optic nerve is 
supposed to decussate or divide itself into two fibres, sending one to the right side 
of the right eye, and another to the right side of the left eye, while a fibre on the 
left-hand side of the optic nerve also decussates, sending one fibre to the left side 
of the left eye, and another to the left side of the right eye. Hence, Sir Isaac 
Newton drew the conclusion, that an impression on each of the two half fibres 
would convey a single sensation to the brain ; and hence, Dr Wollaston con- 
cluded that hemiopsy in one eye must be accompanied with hemiopsy in the other. 

Ingenious as these explanations are, the anatomical facts by which alone 
they could be supported have not been established. Dr Alison, f who has 
adopted the opinion of Newton, and reasoned upon it, admits that the anatomical 
evidence is still defective ; and the late Mr Twining^ has adduced nine cases of 
disease in the optic nerves and thalami, which stand in direct opposition to 
the hypothesis of semidecussation. Dr Mackenzie, too, adopting the same view 
of the subject as Mr Twining, distinctly asserts that " the great mass of facts in 
Pathology and Experimental Anatomy, touching this question, go to prove that 
injuries and diseases affecting one side of the brain, instead of hemiopsia in both 
eyes, produce amaurosis only in the opposite eye." 

The two great facts of hemiopsy in both eyes, and of what is called single 
vision with two eyes, do not require the hypothesis of semidecussation to explain 

* Optics, p. 320. 

f Edinburgh Transactions, vol. xiii. p. 479. 

\ Trans. Med. Soc, Calcutta, vol. ii. p. 151 ; or, Edin. Journal of Science, July 1828, vol. 
ix. p. 143. 



18 SIR DAVID BREWSTER ON HEMIOPSY, OR HALF-VISION. 

them. If hemiopsy is produced by the distended blood-vessels of the retina, 
these vessels must be similarly distributed in each eye, and similarly affected by 
any change in the system ; and, consequently, must produce the same effect upon 
each retina, and upon the same part of it. 

In explaining single vision with two eyes, we have no occasion to appeal to 
double fibres in the optic nerves, or to corresponding points on the retina. There 
is, in reality, no such thing as single vision, that is a single image seen by both 
eyes. With two sound eyes every object is seen double, and it appears single 
only when, by the law of visible position, the one image is placed above the other. 
But even in this case the object is seen double, by means of two dissimilar images 
of it which are not coincident. By shutting the right e}'e, we lose sight of a part 
on the right side of the double image, which is seen only by the right eye ; and 
by shutting the left eye, we lose sight of a part on the left side of the double 
image, which is seen only by the left eye. If one eye gives a better picture than 
the other, the duplicity of the apparently single image is more easily seen. By 
shutting the good eye the imperfect picture is seen, and by shutting the bad eye 
we insulate the perfect picture. It is difficult to understand how optical writers 
and physiologists should have so long demanded a single sensation for the pro- 
duction of a single picture from the two pictures imprinted on the two retinas. 
If we had the hundred eyes of Argus, the production of an apparently single 
picture would have been the necessary result of the Law of Visible Position. 



( 19 ) 



IV. — Miscellaneous Observations on the Blood. By John Davy, M.D., F.R.S., 

Lond. & Ed., &c. 

(Read 6th March 1S65.) 

On a fluid of so much importance as the blood, observations with any preten- 
sion to accuracy can hardly be too often made and repeated, more especially 
when we consider its great instability, its little uniformity, and the differences 
of opinion entertained by physiologists respecting some of its most remarkable 
properties. 

Such is the persuasion which has influenced me in engaging in the present 
inquiry, and in submitting its results to the Society. 

I. On the Action of Water on the Red Corpuscles of the Blood. 

As is well known, the red corpuscles are altered in form and appearance on 
admixture with water, the most obvious change being, that from discs they 
expand into globules. 

In some trials made with the view to ascertain something more precise, I have 
selected the blood of birds, that chiefly of the common fowl and duck, the cor- 
puscles of their blood, from their elliptical shape, being peculiarly fit, as it seemed, 
for the inquiry. 

The first trials made were to ascertain the proportion of water that was 
required to effect any material change. The results obtained were the follow- 
ing :— 

When one measure of water was added to one of serum holding red corpuscles 
in suspension, but few of them experienced an immediate change of form and 
became globular. 

On the addition of two of water, the majority of the corpuscles underwent 
this change, a few only retaining their normal form. 

On the addition of three of water, none of a normal form could any longer be 
seen ; all that were visible were rounded, much reduced in apparent size, and were 
much less distinct ; indeed, a nice adjustment was required to detect them. Many 
of them had a jagged outline ; and from some there was a slight projection, sug- 
gestive of a rupture of their capsule. 

Dried by evaporation at about 100° Fahr., very many of them were found to 
have recovered their original form and size. Some of them, however, appeared 
to be ruptured, the excluded nuclei adhering to their surface; others retained 
their nuclei, of irregular appearance ; all appeared to be wasted. 

VOL. XXIV. PART I. F 



20 DR DAVY'S MISCELLANEOUS OBSERVATIONS ON THE BLOOD. 

On the addition of four of water, the corpuscles were seen less distinctly, yet 
they were to be seen, the adjustment being as accurate as possible, and using a 
warm object-glass, a precaution needed to prevent the dimming of the glass (J, th 
inch power) from the vapour rising from the fluid in such close proximity. 

When more water was added, the only material difference that I am aware of 
was not in the effect on the corpuscles, but in their wider diffusion, thus in- 
creasing the difficulty of observing them. To counteract this, a portion of cruor 
was mixed with water in a tall vessel, stirred occasionally, and after having been 
some hours left at rest, the greater part of the coloured fluid — coloured by the 
solution of the colouring matter of the corpuscles — was drawn off. What remained 
afforded an interesting result. A drop of this fluid under the microscope 
exhibited much the same appearance as that from the addition of four parts of 
water ; and on drying at the same temperature, the appearances were also similar 
but more strongly marked, suggestive of ruptured capsules and the loss of their 
contents, with the exception, as in that instance, of some of them retaining their 
nuclei, these more or less altered. Most of the corpuscles, if that term be applicable 
to their remains, were circular or portions of circles, portions of them having 
been broken of. Some showed a rent, a few wore elliptical, and with the excep- 
tion of being wasted, but little altered in appearance. 

The agency of water on the red corpuscles has commonly been attributed to 
imbibition or endosmosis, to solution of the soluble matter which these cells con- 
tain, and to exosmosis. The appearances which I have described seem to har- 
monise well with this view, with the addition of rupture of the cell-wall or 
capsule, and the occasional exclusion of the neuclei. They accord, too, tolerably 
with those noticed by Professor Lehmann, in his Physiological Chemistry,* with 
the exception of two particulars. He states, that when largely diluted, the cor- 
puscles become invisible under the microscope, which he attributes to their refrac- 
tive power, after the action of water, differing but little from that of water itself. 
As already mentioned, when using certain precautions, I have found them, only 
much less distinct. The other particular relates to their remains. According to 
him, these are mere shreds, and not empty and more or less broken capsules, as I 
have found them to be. The subject, it must be admitted, is one in the investiga- 
tion of which it is not easy to obtain uniform and satisfactory results, there are 
so many interfering and disturbing circumstances concerned, not omitting the 
influence of the serum, and especially keeping in mind the powerful attraction 
the corpuscles have for water, and their hygroscopic properties ; and further, the 
changes to which they are liable as dead matter, from the influences to which 
they are exposed. 

As to the last mentioned, I have found that the longer the blood is kept, the 

* Vol. ii. p. 184. 



dr davy's miscellaneous observations on the blood. 21 

smaller is the quantity of water that is required to alter their form. As to their 
hygroscopic property, this is shown by the simple experiment of breathing on 
them, or by exposing them over water for a few hours, keeping them, of course, 
out of contact with the water. In the instance of the warm vapour of the breath, 
one expiration is sufficient to deprive them, previously dried, of their elliptical 
form. 

It is worthy of remark, that when the corpuscles are coloured by the addition 
of a weak solution of iodine, not only the action of the warm vapour of the 
breath is in a great degree arrested, but even the action of water, and this after 
immersion in water on a glass support for twelve hours, when they were found to 
retain their normal form, only slightly contracted, with their nuclei distinct. May 
it not be conjectured from this, that iodine medicinally used may operate in a 
degree similarly, and thus may arrest undue metamorphic disintegration ? 

II. On the Changes xohich take place in the Blood when excluded from the Air. 
The changes to which the blood is subject when exposed to the air, at ordi- 
nary atmospheric temperatures, are pretty well known. To endeavour to ascer- 
tain what would happen were air as much as possible excluded, the following 
experiments were made : — 

A bottle full of water, deprived of air by the air-pump, was emptied the 
instant before receiving blood from the divided cervical vessels of a barn-door 
fowl ; so soon as full to overflowing, it was closed with a glass stopper lubricated 
with oil, and inverted in water. 

During the first hour the blood retained its original hue, bright vermilion, and 
this throughout. After two hours the colour had lost something of its brio-ht- 
ness. The following day the colour had become uniformly chocolate brown. 
The day after there was no appreciable change. The serum which had separated 
was of a wine yellow, and the crassamentum had contracted considerably. On 
the third day the serum was beginning to show a reddish tinge. From this day, 
viz., the 9th of November, to the 4th of December, the serum became of a darker 
red, and, like the crassamentum, was almost black, as seen by reflected light. 
During the time mentioned, the temperature of the room in which the blood was 
kept varied from about 55° to 58°. The bottle was now taken out of the water, 
which was as clear as at first, showing that the closure was complete. The 
stopper was drawn out with ease, proving— as it was introduced when the blood 
was warm — that there was pressure from within rather than from without, 
though there was no appearance of any gas evolved. The serum decanted was 
of a dark purplish-red, as seen in thin layers by transmitted light, but black by 
the same light, and opaque, in a tube of one-half inch diameter. The crassamen- 
tum, of the same colour, was soft and easily broken up, and had, as well as the 
serum, an offensive putrid smell, but less so than if air had been allowed access 



22 DR DAVY'S MISCELLANEOUS OBSERVATIONS ON THE BLOOD. 

With hydrate of lime, both yielded a strong ammoniacal odour. The blood cor- 
puscles, as seen under the microscope, were found to have become rounded and 
globular. The fibrin seemed to be permanently dyed red ; it retained this colour 
after having been well washed, and after maceration in water for many hours. 
Its structure was finely granular ; it showed no appearance of fibres under gentle 
pressure, and viewed with a high power. 

The experiment was repeated, using the blood of a turkey and also of a 
bullock. The results were similar. That on the blood of the turkey was of the 
same duration as the preceding. That on the bullock's blood was begun on the 
14th of December, and ended on the 7th of January. In the latter instance, 
though no gas was evolved, the putrid blood, when subjected to the air-pump, 
entered into violent ebullition from the copious disengagement of air, and this 
even before the vacuum was nearly complete. It may also be mentioned, that a 
silver probe plunged into the clot became, after a few minutes, strongly dis- 
coloured, indicative thus of the presence of sulphuretted hydrogen. 

A fourth experiment was made with the blood of a duck. In this instance, 
instead of emptying the bottle of water before receiving the blood, the water, de- 
prived of air, was to a certain amount expelled by the blood as it flowed from the 
divided vessels. The specific gravity of the mixture was 1033. After having 
been kept from the 23d. of November to the 12th of January, at a temperature 
varying from about 40° to 50° and 55°, the changes observed on examination 
were so similar to those already specified that they need not be described. 

A fifth experiment was made with the blood of a fowl. As in the last the 
blood was mixed with water; but it differed from the last in being subjected 
to the air-pump as soon as it had become sufficiently cool. No air was thus 
extricated. The bottle was again closed and inverted in water. This was on 
the 16th of February; it was examined on the 17th of March. Some difficulty 
was experienced in withdrawing the stopper. The blood bore marks, of an in- 
cipient putrefaction ; its smell was offensive, and some muriate of ammonia was 
formed on a plate of glass moistened with hydrochloric acid put over it during a 
few hours. 

These results, all so well marked, seem to be nearly identical with those 
which occur when blood of the same temperature is exposed to the air, almost 
the only difference that I am aware of being in degree. The change of colour is 
the same, with the exception, that when exposed to the atmosphere, the blood at 
the surface, especially if it be venous, becomes florid before it darkens ; the change 
of form of the corpuscles is the same, and the solution in the serum of their 
colouring matter. The same gases likewise are formed, and the same alkali is 
generated, accompanied by the characteristic putrid odour. 

That blood should thus undergo change when air is excluded, is no more, per- 
haps, than might be expected when we reflect on its composition, and that oxygen 



DR DAVY'S MISCELLANEOUS OBSERVATIONS ON THE BLOOD. 23 

is contained in it in a state, it is presumed, free to act and give rise to putrefac- 
tive fermentation. 

What is more remarkable is the fact, that blood may be retained in the living 
body, stagnant, at rest, without undergoing similar changes, at a temperature so 
favourable to these changes. I may refer to Hewson's collected works, edited 
by Mr Gulliver, for instances of the kind. In a note, page 17, to mention one, 
the editor remarks, " occasionally blood is extravasated and stagnant in the 
living body for an indefinite time, and yet retains fluidity, as Mr Hunter and 
Mr Caesar Hawkins have noticed." He adds, " I saw a case in a soldier, who 
had received a bruise in his loins, from his horse bolting with him over a bridge 
in Hyde Park ; the injured part quickly swelled, evidently from effused fluid, 
which was let out twenty-eight days afterwards. It measured five ounces, was 
as liquid as blood just drawn from a vein, and coagulated in a cup in less than 
three minutes. The corpuscles were observed to be unchanged, and readily col- 
lected together in the usual way by their broad surfaces. Next day the clot was 
moderately firm, scarlet at the top, somewhat contracted, and surrounded by a 
little serum." What a contrast this presents to the blood from which atmospheric 
air was excluded in the experiments detailed ! Can the difference have been 
owing to the stagnant blood in the living body having been exposed to the action 
of the surrounding tissues, by which it is possible that, though a change may 
have been going on slowly in the blood, the degraded or altered particles may 
have been carried away as they were produced, leaving the residue in its normal 
state? I have witnessed something analogous when a mass of fibrin, enclosed in 
a muslin bag, has been immersed in water under a cock, from which there was a 
constant small stream keeping the water round the included fibrin in motion. 
During about a month that the fibrin was thus exposed at a temperature of 
about 40°, it had undergone little change ; it was firm and only slightly tainted. 
In instances of aneurism, it is well known that not only the fibrin, but also the 
crassamentum enclosed in the sac resist for a long time putrid decomposition. 
May not this resistance be referred to the same cause ? This explanation is sub- 
mitted conjecturally. The fact that extravasated blood, from contusion and vas- 
cular rupture, is commonly absorbed with discoloration of the bruised part, may 
be adduced as somewhat in its favour. The physiologists of the School of Hunter 
would doubtless refer the liquidity of the blood, in the case in question, to the 
vitality of the blood ; but that is a doctrine which at present is hardly tenable. 

III. On the Action of the Air-Pump on the Blood. 
The air-pump I have used in the trials I am about to describe is the same as 
that with which I made some former experiments on the blood,* and, as then, it 
was in excellent order. 

* Anatom. and Physiolog. Res. vol. ii. p. 214. 
VOL. XXIV. PART I. ' G 



24 dr. davy's miscellaneous observations on the blood. 

The chief precautions taken were to receive the blood as it flowed from the 
divided vessels of the animal killed into phials, immediately after they had been 
emptied of water from which the air had been expelled by the action of the air- 
pump, and after closing with a glass stopper, cooling the blood rapidly by im- 
mersion in water. 

Though these precautions were taken, I believe they were not absolutely 
necessary for good results, as I find that when water exhausted of air is poured 
into a carefully washed phial from which water containing air has been poured 
out, on submitting it to the air-pump, no air is extricated either from the water 
or from the side of the phial. 

The experiments on exhaustion have been made on the blood of the common 
fowl, of the duck, of the sheep, bullock, and pig ; they have most of them been 
several times repeated. 

The results have varied more than I could have expected, tending to show 
that the quantity of air extricable from the blood by the air-pump is far from 
constant, and depends on circumstances, some of which are appreciable, others 
obscure. 

1. From the blood of the common fowl, the quantity of air disengaged has 
commonly been less than from that of the duck, sheep, bullock, and pig. 

2. The blood of all the animals, when taken from them shortly after feeding, 
has commonly afforded more air than from animals of the like kind when fasting. 

3. Florid blood, which it may be inferred is chiefly arterial, has yielded less 
air than dark blood, which probablj' is chiefly venous, and, accordingly, that 
which flows first, when an animal has been blooded to death, less than that which 
flows last. 

4. In a small number of instances, those of animals killed after a fast of many 
hours, the fresh blood yielded no air. In some of the trials which gave this 
result, the blood was mixed as it flowed with an equal quantity of water deprived 
of air. 

5. In no instance have I witnessed the disengagement of air from fresh serum, 
proving that the air, when extricated from the blood, is derived from the clot, 
and it may be presumed, from the red corpuscles which are entangled in it. 

6. As might be expected, I have found the disengagement of air from the 
action of the pump more copious in summer than in winter ; and also more copious 
from blood, the fibrin of which has been broken up by having been agitated with 
shot previously freed from adhering air, than from the clot left entire. In the 
instance of the blood of the common fowl, which coagulates rapidly, affording a 
firm coagulum, even the puncturing of it makes a difference ; air then escapes, 
which before was retained. 

7. In many instances, blood which had yielded air on exhaustion, has, after 
exposure for a few hours to the atmosphere, on repetition of the exhaustion, 



DE DAVY'S MISCELLANEOUS OBSERVATIONS ON THE BLOOD. 25 

ceased to yield air, and this when the first trial was stopped before the exhaustion 
of the air was nearly complete. This result, seemingly paradoxical, may have 
been owing to ammonia formed, which may have fixed carbonic acid ; and that 
ammonia was formed, was proved by the hydrochloric test and the production of 
muriate of ammonia. It has been witnessed in the instance of both venous and 
arterial blood, but most remarkably in the latter, and in warm weather oftener 
than in cold. In support of the explanation offered, I may mention an experiment 
on the blood of a calf, which had no food for about twenty hours before it was 
killed. This blood, — it was arterial,— even at first gave off no air on careful 
exhaustion. It was kept under an exhausted receiver from the 23d of April to 
the 13th of May, during the whole of which time it gave off no air, though the 
vacuum was as perfect as it could be made, and the pump was worked daily. At 
the end of this time the serum had become dark red, and on examination the 
blood was found in a state of incipient putrefaction and giving off ammonia. 

What struck me as most remarkable in these experiments with the air-pump, 
was the comparatively small quantity of air, in most instances, disengaged from 
the blood, and its total absence in others, taking into account the quantity of 
carbonic acid liberated in the lungs during life in normal respiration, and also the 
quantity of air, both oxygen and carbonic acid, found in the blood by the German 
physiologists. Difference of temperature, comparing that of the hot blood cir- 
culating in the lungs in birds as high as 106°-108°, and in the sheep, ox, and pig, 
as high as 104°-106°,* with that of the blood of the same animals cooled to 50°- 
55°, may partly account for the result first referred to, but the second adverted 
to I cannot attempt to explain. 

Besides the foregoing trials with the air-pump, I have made some on the blood- 
corpuscles, using very small quantities suspended in serum on a glass support. 
The corpuscles were from the blood of the animals already mentioned, and also 
of the frog and common trout. The results were all nearly similar : so long as the 
corpuscles were floating in serum there was no appreciable change of form, but 
if they were kept some hours under the exhausted receiver until they were left 
apparently dry on the object-glass, then a change was perceptible in them. Under 
the microscope they were found to have become greatly reduced in size, so as to 
be seen with difficulty, and not without the nicest adjustment, and also altered 
in form — the elliptical, as those of the bird, the fish, and batrachian, having 
become rounded. These changes were very similar to those produced by the 
action of water, and they may be accounted for, perhaps, on the idea that they 
were owing to the hygroscopic quality of the corpuscles. I may further remark 
that the effects on the corpuscles of the blood of the several animals tried some- 

* I have found the temperature of the blood of a pig, flowing in a full stream, 106°. The pig- 
was in high condition ; the blood used was from it. 



26 DR DAVY'S MISCELLANEOUS OBSERVATIONS ON THE BLOOD. 

what varied ; it seemed greatest in those of the common fowl, least in those of 
the ox. 

IV. On the Effect of a Loiv Temperature on the Blood. 

It was ascertained by Hewson that the blood, by rapid freezing, is not de- 
prived of its property of coagulating when thawed ;* besides this and the change 
of form of the corpuscles from refrigeration which I have observed,! I am n °t aware 
that any thing has hitherto been published respecting the agency of a low tem- 
perature on this fluid. 

During the frost which prevailed in the Lake District the winter before last, 
from the 2d to the 10th of January, I had an opportunity of renewing the inquiry. 
The blood used was that of the turkey, of the common fowl, and of the sheep. The 
most remarkable result obtained was that a low temperature, like a high tempe- 
rature, appears to promote not only a change of form of the red corpuscles, but 
also a change of composition, as indicated by the production of ammonia and the 
solution in the serum of the colouring matter of the blood. As the changes were 
the same whichever blood was the subject of experiment, I shall restrict myself 
to what was observed in the trials on that of the common fowl. On the 4th of 
January a wine-glass was nearly filled with the blood of a full-grown fowl as it 
flowed from the divided great cervical vessels; it coagulated in less than two 
minutes. A plate of glass, moistened with a drop of dilute hydrochloric acid, 
was placed over it. After ten minutes there was a copious deposition of dew r on 
its inner surface, vapour from the warm blood beneath, and there condensed. On 
examination w r ith microscope, after evaporation, not a trace of muriate of am- 
monia could be detected. The trial was repeated, and for six hours in the open 
air, at the temperature of 28° Fahr. ; now a trace barely of the salt was found 
The blood was moderately florid, preserving its original appearance, and was not 
yet frozen. It was left out during the night. The temperature during the time, as 
shown by a register thermometer, was as low as 12° ; on the following morning, 
at a.m., it had risen to 18°. The blood was found to be frozen hard and 
thoroughly ; it was greatly darkened in colour, and had lost entirely its florid 
hue. Distinct crystals of muriate of ammonia, and these not a few, were detected 
on the covering glass after the evaporation of the acid, and the red corpuscles 
from elliptical had become circular and globular. 

The observations were continued until the morning of the 10th, when a thaw 
set in. The blood was examined twice daily, viz., at 9 a.m. and at 3 p.m. During 
the period the temperature was always below 20°, but not lower than 15°, excepting 
once, as already mentioned. The day temperature ranged as high as 27°, it was 
never lower than 22°. At the former temperature, a softening of the blood was 

* Hewson's "Works, p. 25. 

f Physiological Researches, p. 369. 



DR DAVY'S MISCELLANEOUS OBSERVATIONS ON THE BLOOD. 27 

observed from incipient thaw. During the whole time, as denoted by the test 
employed, ammonia was evolved, and, as well as I could judge, the lower the 
temperature the larger was the quantity. I need hardly remark that there was no 
appreciable contraction of the crassamentum, no further separation of serum after 
congelation had taken place. The serum which first exuded before congela- 
tion—a very small quantity— after having been frozen, became coloured, and, 
finally, of a red nearly as dark as the general mass, and this owing in part 
to blood corpuscles suspended in it of altered form, and in part to solution of 
their colouring matter. After thawing, the blood had no smell indicating pu- 
tridity, nor did it discolour silver ; yet it continued, at a temperature of 50°, to 
evolve ammonia, and much in the same proportion as when frozen. Now, how- 
ever, the contraction of the crassamentum, i.e., of its fibrin, before arrested, took 
place, and to an extent seemingly differing but little from what would have 
occurred had the blood not been frozen. The blood corpuscles now were so 
reduced in size, and had become so transparent, that unless dried, they were seen 
with difficulty, and not without the most accurate adjustment. 

These results, viz., the disengagement of ammonia, and, we must infer, its 
formation, when blood is frozen, are hardly such as could be expected ; and they 
are the more remarkable, as seeming to be independent of putrefaction and the 
action of oxygen, and owing to a new arrangement of elementary parts produced 
by a low temperature, one ranging from about 50° to many degrees below the 
freezing point. That congelation was not essential to the formation of the 
ammonia was shown in other experiments, in which, when blood was exposed to 
a temperature ranging in one trial from 32° to 34°, the volatile alkali was pro- 
duced, and in others at a temperature varying from 40° to 50° ; and, in the latter, 
even when continued several days, without any indications of putridity, judging 
from the absence of the smell such as denotes putrefaction, and from silver 
immersed remaining untarnished. 

At first view what has been described may seem anomalous, yet the results 
are not without analogies. The potato, as is well known, becomes sweet from 
the conversion of starch into sugar by " frosting ;" and the ripening of the grape, 
the sweetening of its juice, it is also well known, is hastened by the setting in of 
frost at the time of the vintage in Switzerland, and in other countries with a 
similar climate. The formation of peat is another example of the efficiency of a 
comparatively low temperature in producing new compounds. Familiar with the 
effects of heat — i.e., of a high temperature— as an active agent, it is not perhaps 
surprising that cold — i.e., a low temperature — should be little thought of except 
as the opposite and the antagonist of heat, disregarding the fact that they differ 
merely in degree; and how inconsiderable that is, whether measured by our 
sensations or by the thermometer. 

After witnessing the effects of congelation on blood, the question occurred, Is 

VOL. XXIV. PART I. H 



28 DR, DAVY'S MISCELLANEOUS OBSERVATIONS ON THE BLOOD. 

meat liable like it to change from freezing — that change which the evolution of 
ammonia indicates ? As it is well known that meat may be kept for weeks frozen 
without being spoiled as an article of diet, the obvious answer was in the nega- 
tive. The only experiments I have made have afforded results leading to the 
same conclusion. A portion of fresh mutton, cut into small pieces, was exposed 
on the b'th of January to the open air. During the following night the register 
thermometer was as low as 10° ; the next morning it was 22°. The meat was 
not frozen ; its fibre was soft and flexible ; a bare trace of muriate of ammonia 
was found on the glass above it prepared as a test of the volatile alkali. Before 
night it became frozen and rigid, and it continued so until the thaw began on the 
10th. Examined twice daily, no traces could be detected of the production of 
ammonia. The fibre, indeed, was evidently softened, and its striated structure, 
as seen under the microscope, was less conspicuous, so much so, that without a 
good light and a careful adjustment it could not be seen. 

A like question occurred respecting manures — Does frost arrest their decompo- 
sition ? I have made trial of stable-dung, and have found it when frozen to 
exhale ammonia in an unmistakable manner, proving that a low temperature, as 
in the instance of blood, promotes its decomposition, or that change on which the 
evolution of ammonia depends. A similar result has been obtained from the 
exposure of impure lithate of ammonia (the urinary excrements of the pelican), 
of the mixed excrements ; partly urinary, partly alvine, of the barn-door fowl, 
and of guano. From all of them, using the same test, the production of ammonia 
was conspicuous. Should not these results suggest the propriety of reconsidering 
the treatment of manures, and if not the time of their application to the land, at 
least whether an addition should not be made to them to fix the ammonia ? 

V. On the Action of Ammonia on the Blood. 

Since the hypothesis has been advanced, that the escape of ammonia from the 
blood is the cause of its coagulation, additional interest is attached to the action 
of the volatile alkali on this fluid. 

The following experiments have been made with a view not so much to test 
the correctness of that hypothesis, as to show what are the effects of ammonia on 
the blood as a whole, and on its several parts : — 

1. On the Entire Blood. — On the 8th of December 241 grs. of the blood of a 
duck were received, as it flowed from the divided cervical vessels, into a bottle 
containing 72*5 grs. of aqua amnionic of sp. gr. -95. The bottle was immediately 
closed with a glass stopper. This was at 10.37 a.m. At 12.15 p.m. a semi-fluid 
viscid coagulum had formed, of a rich Turkey-red colour. A glass rod applied to 
it, it yielded to gentle pressure, without adhering to, or in the slightest degree 
soiling the rod. At 2.30 p.m. it was somewhat firmer. At 10 p.m. it was more 



DR DAVY'S MISCELLANEOUS OBSERVATIONS ON THE BLOOD. 29 

so ; now, when the bottle was turned on its side, it ceased to flow. On the fol- 
lowing day it was so firm that it bore inversion without flowing ; no serum had 
separated. Examined on the 13th of December, the only change perceptible was 
that it was rather firmer. On the 1st of January it was more carefully examined. 
On withdrawing the stopper, as might have been expected, the smell of the 
ammonia was very powerful, indeed unendurable. The coagulum was found 
of the consistence of a pretty firm jelly, readily yielding to pressure, but not 
adhering to the glass rod impressing it. The whole mass was easily removed, 
retaining its form unbroken ; and such was the adhesiveness of its substance — 
i.e., of its particles to one another — that the mass admitted of being divided with 
a scissors without its soiling the instrument. A portion of it put into water did 
not immediately colour the water ; from black it became dull brown. Examined 
with the microscope under compression, it exhibited a finely granular surface, 
through which were scattered globules of a less diameter than the blood corpuscles 
— these, it may be inferred, contracted. 

In other experiments, made within a few days of each other, with smaller 
proportions of the volatile alkali, the effect has been found to vary. 

When 12 grs. of aqua ammonite, of the same strength as that last mentioned, 
were mixed with 465 grs. of the blood of a turkey, the instant it was shed, the 
coagulation was retarded about 20 minutes. On withdrawing the stopper the 
following morning there was a strong smell of ammonia ; the crassamentum was 
found of tolerable consistence, and was surrounded and covered with red serum, 
which owed its colour chiefly to red corpuscles suspended in it of a globular form, 
a change from their normal form evidently owing to the action of the alkali. 
Examined again after twenty days the coagulum was found firmer ; it admitted 
of being taken out as an entire mass. 

In a third experiment 2 - 5 grs. of aqua ammonise were mixed, as in the former 
instances, with 572 grs. of the blood of a fowl. After two hours the blood was found 
feebly coagulated and viscid, in a semifluid state, sluggishly flowing like tar. 
When a portion of it was poured into water, it did not mix with the water, but 
kept entire, retaining its viscidity. What remained, examined the following 
morning, was found divided into a somewhat denser crassamentum, still semi- 
fluid and viscid, and a red somewhat viscid serum, abounding in red corpuscles, 
more or less altered in form, many of them .diminished in volume, and almost all 
of them rounded. Both the soft coagulum and the serum smelt of ammonia. 

A fourth experiment was made on the blood of a sheep, after the same manner 
as the preceding. The quantity of the aqua ammoniae was 1 gr., of the blood 587 
grs. Examined after about half-an-hour, the blood, still warm, was found pretty 
firmly coagulated, and already some serum had separated. The glass stopper was 
withdrawn, and instantly after a plate of glass, moistened with dilute hydro- 
chloric acid, was placed over the mouth of the bottle, and left for two minutes. 



30 dr davy's miscellaneous observations on the blood. 

Now, after evaporation, crystals of muriate of ammonia, of a large size and in 
abundance, were found on it. 

A fifth experiment, similar in manner to the last, with the exception that the 
aqua ammonise (1 gr.) was spread as much as possible over the inside of the 
phial, was made on the blood of a fowl (590 grs.) The blood coagulated in eight 
minutes, and pretty firmly. Another portion, caught in a wine-glass, coagulated 
in about a minute. Each was tested for ammonia, as in the preceding trial. 
The blood in the wine-glass, after five minutes — the time that the acid was kept 
over it — afforded no distinct trace of ammonia. The blood in the bottle, after 
one minute, afforded ample proof of the evolution of ammonia in the large 
crystals of the muriate which were formed on evaporation on the incumbent 
glass. The contrast, indeed, was very striking, comparing the blood with and 
without the addition of ammonia, as thus tested, and also by test-paper ; the 
one, the former, having no effect during a minute that moistened test-paper was 
held over it; the other, in the same time, producing a decided alkaline reaction. 
On the following morning the crassamentum in the bottle was found slightly 
contracted, though less than that in the wine-glass ; some reddish serum had 
separated ; the blood corpuscles, whether suspended in the serum or retained in 
the clot, were little if at all altered. 

From these experiments it would appear that the effect of aqua ammonia? 
varies as to the quantity used, and this in a manner that could hardly be ex- 
pected ; 31 per cent, occasioning a thick adhesive coagulum, with a change of 
form of the red corpuscles, without the separation of any serum ; 25 per cent, 
retarding the coagulation many minutes, but not preventing the separation of 
serum and a certain contraction of the crassamentum ; 0*44 per cent, retarding 
the coagulation and rendering the coagulum soft and viscid, barely semifluid, with 
little separation of serum, and that viscid; lastly, 017 per cent, had little effect, 
except that of retarding for a few minutes the coagulation, — the coagulum, when 
formed, having very much its normal appearance. 

2. On the Fibrin of the Blood. — The fibrin used was obtained by washing the 
clot which had formed in the first experiment. In its moist state it was slightly 
viscid. By drying it lost 93 per cent. ; 25 grs. thus dried were put into a phial 
with 273 grs. of aqua ammonias of sp. grav. -89, and secured by a glass stopper. 
After eleven days it was not apparently diminished in volume : 41 grs. of the 
clear fluid decanted and evaporated yielded only 1 gr. As the fluid became con- 
centrated during the process, which was conducted at a low temperature, its 
fluidity diminished, and when reduced to a drop it was still transparent. In its 
dry state it appeared as a transparent film, and as seen under the microscope 
with a high power it had a finely granular appearance. 

A second experiment was made on the same fibrin in its moist state, using in 
place of aqua ammonise alone a dilute solution, consisting of 654 grs. of the alkali, 



DR DAVY'S MISCELLANEOUS OBSERVATIONS ON THE BLOOD. 31 

and of 305 grs. of water. The fibrin was equal to 31 grs. After ten days its 
volume seemed little diminished — 58*4 grs. of the clear fluid evaporated left -1 gr. 
The undissolved residuary portion, constituting so large a proportion of the whole, 
was soft, glutinous, and adhesive ; it might be called ropy, as it allowed of being 
drawn out, and when agitated by a circular motion, it rose spirally in the liquid. 
It thus differed from the dried fibrin, which was softened in a slight degree, but 
not rendered glutinous. Examined after thirty-four days, it seemed little altered 
in bulk, and nowise in its properties. The fluid was slightly viscid : a portion 
of it, 41 - 4 grs., evaporated to dryness, yielded only 05 gr. It became slightly 
turbid during evaporation at a temperature of about 180°, and when the ammonia 
was driven off, it lost the little viscidity it before had. The smaller proportion 
of residue in this instance might have been owing to the circumstance that the 
phial holding the fibrin and the dilute aqua ammonise not being firmly corked, 
some of the ammonia might have escaped. 

These results demonstrate how feeble is the solvent power of ammonia on 
fibrin. Many other experiments which I have made, of which an account is 
hardly needed, have been amply confirmatory of the fact, and also of the well- 
known effect of ammonia in rendering fibrin viscid and glutinous, and of increas- 
ing its transparency. This last effect should be kept in mind, otherwise, as the 
refractive power of fibrin differs but little from that of water, it may in some 
instances be imagined to be dissolved, when it is only diffused.* 

3. On the Serum of the Blood. — On this fluid the effect of ammonia is less 
distinct. It appears to diminish rather than to increase the viscidity of the 
serum, as is shown by the following experiment : a portion of the serum of the 
blood of a pig, equal to 314 grs., was mixed with 274*4 grs. of aqua ammonias of 
sp. gr. -89, in a glass-stoppered phial ; and about an equal quantity of the serum 
of the same blood was poured into a similar phial. This was on the 30th March. 
Each was shaken daily : froth was produced in each instance, but that from the 
ammoniacal mixture subsided more rapidly than that from the serum alone ; and 
the longer the trial was continued — it was continued more than a month— the 
more marked was the difference. 

At the end of this time the ammoniacal mixture had deposited a white 

* When well-washed fibrin, still slightly coloured by the colouring matter of the blood, is placed 
under the microscope, it appears to consist of translucent granules forming under gentle pressure a 
connected tissue. On the addition of aqua ammonise it becomes clear and transparent, like jelly, 
with a brightening of its colour. Compressed, it shows elasticity, and when extended by continued 
pressure, so as to be very thin, its appearance is hyoloid ; no granules are to be seen in it except a 
few scattered ones, which, it may be, were derived from blood corpuscles. 

Fibrin which has been rendered viscid by ammonia, after the removal of the ammonia by repeated 
washing, gradually contracts, and from being transparent becomes, in consequence of condensation, 
opaque, or nearly so. Thus contracted it often exhibits an imitative form, like that of hydatids. Its 
retention of the colouring matter of the blood is remarkable ; it is greater even than that of the 
capsule or walls of the corpuscles. 

VOL. XXIV. PART I. I 



32 DR DAVY'S MISCELLANEOUS OBSERVATIONS ON THE BLOOD. 

matter, which was readily diffused on gentle agitation, rendering the fluid, which 
was before transparent, turbid. 

Under the microscope the deposit exhibited thin crystalline plates, their 
length exceeding their width about a third, some minute spicula, somewhat like 
raphides, and some granules. As the matter was not viscid, it may be inferred 
that fibrin did not form a part of it. 

The transparent fluid separated by decantation from this sediment yielded a 
coagulum with the sulphuric, muriatic, nitric, and acetic acids, added each in 
slight excess, that is, in a quantity a little more than was sufficient to neutralise 
the ammonia. The precipitate was redissolved by the sulphuric and muriatic 
acids, and in great part by the nitric —these acids concentrated — but not by 
the acetic. 

When the clear ammoniacal fluid was boiled until the whole of the volatile 
alkali was expelled, it was rendered gelatinous, that is, the coagulum formed was 
soft and transparent, like the albumen of the eggs of some birds similarly treated. 

The same fluid, evaporated at a low temperature, left a brownish transparent 
matter, which was soluble almost entirely in water. The solution frothed when 
boiled and gelatinised. It had a slight alkaline reaction, like serum, and had no 
unpleasant smell. Evaporated again, little of it was redissolved on the addition 
of water, and still less on repeating the operation — thus resembling ordinary 
serum.* 

The serum without the addition of ammonia, kept during the same time, had 
also yielded a deposit, which was of a greyish hue, and under the microscope 
exhibited only amorphous particles The fluid had acquired a reddish hue, and 
had an offensive putrid smell, and it afforded when boiled a firm coagulum. 

Comparing, then, the two, it appears that ammonia renders serum less 
viscid, prevents its putrefaction,! and modifies in some degree its coagulable pro- 
perty. Whether the serum of the blood of other animals under the influence of 
ammonia would show the same properties, I have not ascertained with sufficient 
accuracy. From the few comparative trials I have made, I am disposed to infer 
that there would be no material difference. 

4. On the Red Corpuscles of the Blood. — On these the effect of the volatile 
alkali is more decided, as is shown by the following experiment,— one of the 

* Serum of blood, such as I have tried, and I have made many trials, on first evaporation affords 
a residue which is almost entirely soluble in water, but on repetition again and again, it is so altered 
as to become insoluble. 

f Ammonia does not appear to arrest entirely the putrefactive decomposition of the blood : 
thus a mixture of 257 grs. of blood, and of 2 - 5 grs. of aqua ammonia;, the subject of the third expe- 
riment, after having been kept twenty days, had, besides an ammoniacal odour, an offensive smell, 
indicative of incipient putrefaction. In great excess, it certainly retards the change in the instance of 
the entire blood, and in a great degree in the instance of the fibrin, and in that of the serum. A 
portion of the coagulum left from the first experiment and kept three months, had, after the ammonia 
had been rapidly expelled, an offensive odour, only in a slight degree. 



DR DAVY'S MISCELLANEOUS OBSERVATIONS ON THE BLOOD. 33 

many which I have made. The cruor used was from fresh bullock's blood, its 
fibrin separated in the usual way ; 45 grs. of it were mixed with 48 grs. of aqua 
ammonise. The colour was immediately darkened, so much so, that by reflected 
light it appeared almost black ; by transmitted, of a garnet-red, similar to the 
change of colour observed when the entire blood was used, and it was accompanied 
by the same alteration in the corpuscles, these being reduced in size and rendered 
globular. Another obvious effect was an increase of viscidity. Examined after 
eight days, and again after twenty-four, the only further change noticeable was 
the disappearance of the corpuscles, as if they had in great part been dissolved ; 
they were not to be seen under the microscope ; minute granules only were 
visible, and these were seen only after evaporation. 

It is worthy of remark, that when the whole of the volatile alkali was expelled 
by heat at a temperature below 1 60°, and the residuary fluid was tried by test-paper, 
only the feeblest alkaline reaction was observable ; in this respect, differing from the 
serum, which under the same circumstances showed a distinct alkaline reaction. 
The solution was coagulated at a temperature of about 160°. Another portion 
evaporated at a low temperature was resoluble, i.e., the colouring matter; seeming 
to show that this matter had suffered no change from the action of the volatile 
alkali. 

The bearings of the results of these several experiments on the hypothesis 
adverted to, hardly need be dwelt on, they are so obvious. Seeing that ammonia, 
in so large a quantity as that used in the first experiment, did not prevent the 
coagulation of the blood, or, in other words, of its fibrin — its coagulable part — it 
would be strange, indeed, if the escape of a very minute quantity of the volatile 
alkali, hardly an appreciable one at most, should be the cause of the phenomenon. 

Considering that ammonia renders the fibrin viscid and alters the shape of the 
red corpuscles, is there not ground for caution as regards its medicinal use, and 
of more than doubt of its efficacy when administered with the intention of dis- 
solving a coagulum in cases of thrombosis ? The marked difference as to alkaline 
reaction of the serum and cruor, as already mentioned, was suggestive of analogy 
between the blood and the contents of the egg. It is stated that an aqueous 
solution of the colouring matter of the former is neutral.* Whatever care I have 
taken in preparing it, draining off the serum as much as possible from the clot 
before the action of water, I have always found it feebly alkaline.f Nor is this 
surprising, considering the impossibility of getting rid of all the serum by drain- 

* Bra.nde and Taylor's " Chemistry," 1863, p. 833. 

f In one experiment, the clot, from six ounces of bullock's blood, after draining off as much as 
possible of the serum, was cut into small pieces and macerated in water, using the ordinary means to 
separate the fibrin. The solution formed, loaded with colouring matter, was evaporated at a temper- 
ature below 160°, until reduced to the sp. gr. 1033 ; its alkaline reaction then was very slight, so as 
to be hardly discernible when the delicate test-paper used was dried. 

After evaporation of the solution to dryness, the residue was exposed to the fire in a platina 
capsule. In its charred state, after it had ceased to burn with flame, its particles were slightly 



34 dr davy's miscellaneous observations on the blood. 

ing. Further, I have found the ash of hsematine prepared by a more elaborate 
process also feebly alkaline ; and the latest analyses of the several ingredients of 
the blood, those most to be depended on, indicate the same.* May not this 
difference, slight though it appears, warrant the conjecture, that as in the egg, so in 
the blood, there may be an action of a galvanic kind between its several proxi- 
mate parts ? And may not the differences which are known to exist between the 
serum and the red corpuscles be adduced in favour of the conjecture? 

VI. On the Coagulation of the Blood. 

Of the many hypotheses which have been advanced at different times to 
account for the coagulation of the blood, each has been supported, as hypotheses 
usually are, by some facts, but few of them have for any length of time main- 
tained their ground, facts having been adduced hostile to them. 

Of the latest hypotheses brought forward, one is that of Dr Richardson, 
briefly designated the ammonia-theory, to which I have already adverted ; 
another is that of Professor Lister, in which he considers the phenomenon as 
mainly depending, out of the body, on a kind of catalytic action produced by the 
contact of any foreign substance, and, within the body, as owing to an analogous 
cause, contact with a part, either dead or quasi dead, — as he supposes a tissue to 
be under the influence of inflammation.! 

This hypothesis, as it appears to me, is open to certain objections. I shall now 
notice merely a few of the facts which seem to me most opposed to it. 

1 . Were it true, ought not the phenomenon of coagulation to take place in every 
instance in which dead matter comes in contact in the living body with the blood ? 
Instances of ossification, in which concretions of phosphate of lime are formed in 
the arterial coats, and often project into the vessels themselves, — concretions 
differing but little from the " tartar," deposited so often on the teeth, and in- 
organic, — are familiar to every one acquainted with pathological anatomy, and 
yet in the majority of these cases the coagulation of the blood has not taken place 

2. In instances of aneurism, with a rupture of the vessel, the seat of it, a 
coagulum of blood is invariably formed, though in contact with parts which, it 
may be presumed, until the contrary is proved, still retain their vitality. 

3. Examples of the coagulation of the blood in the veins, in the arteries, and 
in the ventricles of the heart, during life, in persons reduced to a feeble state by 

attracted by the magnet, the coal after cooling having been reduced to powder. The particles of its 
ash, after the charcoal had been burnt off, were also similarly attracted. The magnet used, it may 
be .mentioned, was a needle that had been magnetised by a foetal torpedo, and which (as the result 
showed) still retained its power, after the elapse of 32 years. The residuary ash, on the addition of 
a little water, showed so feeble an alkaline reaction, that it was hardly as well marked as that of the 
saliva. 

* Lehmann's " Physiological Chemistry," ii. pp. 160, 212. 

f Proceedings Roy. Soc. Vol. xii. p. 580. 



dr davy's miscellaneous observations on the blood. 35 

disease, are not of unfrequent occurrence, and this often without any apparent 
lesion in the coats of the vessels themselves, or in the lining membrane of the 
ventricles. 

4. Confirmatory of the last, many examples are on record of the blood, in its 
coagulated state after death, having been found broken up in the left ventricle of 
the heart, proving that its coagulation must have taken place whilst the heart 
was still forcibly acting, and this in cases in which the organ appeared to be 
sound* 

5. Certain poisons influence the coagulation, some accelerating it, some retard- 
ing it. As an example of both, may be mentioned the poison of a snake, the 
tic-polonga of Ceylon (Daboia Bussellii, Gray), which on fowls acts with extreme 
rapidity, so much so, that simultaneously with their death, it occasions the 
coagulation of the blood in the heart and great vessels, and this even before the 
former has ceased to act ; whilst, in larger animals, such as the dog, in which it 
takes effect less rapidly, causing death in an hour instead of about a minute, it 
has a contrary influence, that of preventing the coagulation of the blood.f There 
are other considerations which seem to me to cast a doubt on the accuracy of this 
hypothesis. To reconcile it with certain facts, its author is under the necessity 
of assuming that a clot is a " living tissue in relation to the blood ;" if so, then 
does it not follow, in strictness of reasoning, that such must be its state under all 
conditions, whether formed within the body during life, or in blood abstracted by 
the ordinary operation of blood-letting ; and he is further under the necessity of 
assuming that inflamed parts are quasi dead parts, or, in other words, — and they 
are his — " have lost for a time their vital properties, and comport themselves like 
ordinary solids." 

The vagueness, moreover, of the hypothesis renders it open to objection. The 
referring the phenomenon to a catalytic action, seems to be little more than the 
accounting for what is obscure by that which is equally or hardly less obscure. 

To conclude, I fear it must be confessed that, strictly speaking, the theory of 
the coagulation of the blood, its vera causa, is still an unsolved problem, there 
being, to all the hypotheses which have hitherto been propounded, opposing facts 
logically in strictness prohibiting the establishment of any one of them. 

* Seethe author's Anatom. and Physiolog. Research., ii. 196. f Idem, vol. i. p. 123. 



VOL. XXIV. PART I. K 



( 37 ) 



V. — A Study of Trilinear Co-ordinates : being a Consecutive Series of Seventy - 
two Propositions in Transversals. By the Rev. Hugh Martin, M.A., Free 
Greyfriars', Edinburgh. Communicated by Professor Kelland. 

(Read 20th March 1865.) 

Introductory Remarks. 

The following series of theorems is given as an illustration of the modern 
method of trilinear co-ordinates, having been wrought out after perusal of Mr 
Ferrar's very lucid and elegant treatise on that subject. The demonstrations 
present no difficulty, requiring nothing more complicated than the formation of 
determinants of two and three places. Accordingly, after exhibiting the method 
of proof in a few instances, I have merely given the enunciations of the remaining 
propositions. As the series of theorems advances the manipulation becomes, of 
course, a little more complicated ; but the co-ordinates and co-efficients always 
appear in such symmetry as very greatly abbreviates the task, and guarantees 
its accuracy. Two, or perhaps three, of these seventy-two theorems are known 
mathematical truths ; but that so many new consecutive propositions should be 
so easily found, and so easily proved, is a convincing evidence of the simplicity, 
fertility, and power of this new and beautiful method. 

Treated according to the ancient geometry, the contents of the following pages 
would constitute a volume of no mean dimensions ; and some of the propositions, 
such as those which affirm that the six points P lf P 2 , P 3 , P 4 , P., P G range in a 
straight line, and that the seven straight lines U^; R X R 2 , R 3 R 4 ; S^, S 3 S 4 ; 
QiQ 3 , Q-iQ^i Q 2 Q 6 a ^ meet m a P omt 5 would probably have been undiscoverable. 

In the admirable treatises of Mulcahy and Townsend a few analogous propo- 
sitions are demonstrated geometrically. Mr Townsend, in particular, has a 
chapter in his first volume, on concurrent lines and co-linear points, which falls 
in very closely with the kind of propositions which the following series embraces. 
His second volume I have not been fortunate enough to see ; but the subject is 
only ripening for a systematic gathering-up of the propositions that have been 
discovered in this line of investigation, and the following pages are presented as 
a humble contribution towards that desirable result. 

A word or two may be permitted in reference to the additions to the termin- 
ology which must be made, and generally sanctioned by mathematicians, ere such 
systematic digest can be successfully accomplished. I have ventured — of course 
only provisionally — on one or two such additions. When the co-ordinates of two 
points are respectively the algebraical inverses of each other, I have called these 
points, in reference to each other, " inverse points ;" and it is evident that a very 

VOL. XXIV. PART I. L 



38 REV. HUGH MARTIN ON TRILINEAR CO-ORDINATES I 

fine vein of mathematical truth opens up in reference to them, which it needs 
only a little ingenuity to work advantageously. Thus, at a glance, it is evident 
that if a point moves in the straight line la+m (3+ny=0, its inverse moves in 

the locus, — + -a + — =0; which is a conic passing through the angular points of 
ci p y 

the triangle of reference. Since writing the following pages I find Mr Townsend 

has a chapter entitled " Theory of inverse points with respect to a circle ;" and 

although not treated according to the trilinear method, these points, so called, 

will be found, I rather think, if so treated, to present only a case of what I have 

called "inverse points" in general. In the same manner I have called two lines 

" inverse" with respect to each other when the co-efficients of the co-ordinates 

are respectively the algebraical inverses of each other. 

There is another relation between a special point and line which I have not 
ventured to designate, but to which I would respectfully call attention as requir- 
ing designation. When lines from the angular points of a triangle are drawn 
through any point to intersect the opposite sides, the intersections constitute 
the angular points of an inscribed triangle, whose sides are known to meet the 
corresponding sides of the original triangle in points which range in a straight 
line. Instead of giving a particular designation to this line, I have used the 
general functional symbol ; and, as its position depends exclusively on the point 
— say P, I have called the line <p (P), in a few theorems in reference to it (Theorems 
XXXI. — XXXV.) . Of course the inverse functional symbol (p ~ l indicates the point 
in reference to the line, as the direct symbol indicates the line with reference to 
the point. This point and line are, indeed, with respect to each other, a species 
of pole and polar, — the line being the ordinary polar, not of the point but of its 
inverse, — to the imaginary conic a 2 +/3 2 +7 2 =0. Manifestly a special designation 
is necessary in a case like this, in order to secure that ease of reference and that 
brevity of treatment without which the pioneering work of farther investigation 
is brought to a stand. 

Theorem LXVI. is the prize question of the " Gentleman's Diary" for 1841; and 
some long but good geometrical demonstrations of it are given. The proof is per- 
fectly simple according to the trilinear method, and the co-ordinates of the point 
appear in a form so elegant that one could not help seeing that it must have some 
singular relations and be worthy of a name. I have accordingly ventured to call 
it the Anapole of the two given points ; and, connecting it with some of the pre- 
ceding results, I find a few propositions easily deducible, such as that the anapole 
of two inverse points and the line joining them are pole and polar, to the imaginary 
conic, a 2 + j3 2 + y 2 = 0. For the three concluding theorems I am indebted to a young 
mathematical friend — destined, I believe and trust, to scientific eminence — Mr 
George M. Smith, student in the Aberdeen University. On proposing to him the 
problems of finding the locus of the anapole of a central body and its planet, and 



SEVENTY-TWO CONSECUTIVE PROPOSITIONS IN TRANSVERSALS. 



39 



the locus of the anapole of two points which should move away from each other 
in a straight line with uniform velocities, I was delighted to receive demonstra- 
tions, perfectly simple and elegant, to the effect that, in the former case, the ana- 
pole moves in a straight line, let the planet move as it may ; and that, in the latter 
case, the locus of the anapole is a conic section, and becomes a straight line if the 
uniform velocities are equal ; and farther, that the anapole of any two points 
in an ellipse circumscribing the triangle of reference is invariable. Geometers, I 
am sure, will admire these theorems of a rising young mathematician, and will 
recognise the vein thus struck as promising to be a fertile one. Mr Smith added 
another very beautiful property of the anapole, which turned out, on investigation, 
to be identical with Theorem LXV. of the following series. 



Instead of defining a point by the equations y=£-=^, we shall say the point 

is — (/, m, n). Instead of defining a straight line by the equation la+mj3 + ny—0, 
we shall say the line is — (I, m, n). 

The straight line joining the points (l v m lt n^, (£ 2 , m 2 , n 2 ) is; — 



m 2 , n 2 


» 


n v l 2 


3 


l v m 1 

l 2 , m 2 



The intersection of the two straight lines (l v m ± , n t ), (l 2 , m 2 , n 2 ) is defined by 
the same expression. This identity of form is, in reality, the earliest germ of the 
doctrine of pole and polar ; and gives rise to what is usually regarded as the first 
promise of that doctrine, namely, the identity of the condition that the three 
points (l lt m v w x ), (l 2 , m 2J n 2 ), (l s , m 3 , n s ) shall range in a straight line, with the 
condition that the three straight lines (Z 15 m x , ra x ), (l 2 , m 2 , n 2 ), (l s , m s , w 3 ) shall 
intersect in a point ; which is, in both cases, 






= o. 



THEOREMS. 

Theorem 1. 

On the sides of the triangle A B C, as bases, are constructed three triangles, 
A X B C, A BjC, A B C 15 similar to each other, and so placed that the angles 
A 1 BC = AB 1 C = ABC 1 ; B,C A = B C^B C A, ; and C 1 AB = C A^C AB r 
Then A A v B B x , C C x meet in a point. 

The sides of ABC, taken as the triangle of reference, being a, b, c, the per- 
pendiculars from Aj on a, b, c are, respectively, 

a . sin B x . sin C x a . sin B x . sin (C + C x ) a . sin C t . sin (B + B 2 ) 



sin A, 



sin A, 



sin A, 



40 



REV. HUGH MARTIN ON TRILINEAR CO-ORDINATES 



Hence the trilinear co-ordinates of A x are 



of B x are 



-1, 



sin (C + Cj) 



sin C x 



sin (C + CJ sin (B + B ,) 
sin C 2 sin B y 

sin (A+AJ 

sin A, 



of C x are 



sin f B + B,) sin (C + C,) 
sin B x sin C t 



-1. 



sin(A + A.) sin(B + B.) sin (C + C.) u _. . m . 
For ;• T > .. I * » . I , P^/, g,A. Then;— 



AAj is 
BBj is 
CC X is 



sin A 



sin B 



sin C, 



A x is — 1 



h, g.^ r A is 1, 0, 0. ^ 

~B[ is h, -1, /.I. Also, -J B is 0, 1, 0. I Hence ;- 
C^s g, f -l.J (Cis 0, 0, l.J 



0, g, -h. 

-/, 0, h. 

/, ~9, 0. 



= 0. Therefore A A v B B p C C l intersect in a point — say P,. 
V 1 is gh, hf,fg, or f~\ g~\ h~\ 



Theorem 2. 



B^ is 1-f, h+fg, g + hf 
C 1 A 1 is h+fg, l-g 2 , f+gh 
A^j is, g + hf f+gh, 1-A 2 



Also, 



BC is 1, 0, 0. 

CAis 0, 1, 0. 
AB is 0, 0, 1. 



B C, B 1 C 1 meet in 2^ which is 
CA, C 1 A l „ 3S X „ 



AB, A^ 



0, 9 + V, -(>>+/</)• 

-(f+9fy 0, A+/S'- 



Hence ; - 



= 0. Therefore ;- 



l^^ is a straight line, viz., (f+gh)- 1 , (g + hf)~\ (h+fg)- 1 . 



BCjisl, 0, g 
CA^sA, 1, 
ABjisO, / 1 



AA 


is 


B 


B, 


is 


C 


c 2 


is 



Theorem 3. 



Also 



B^is 1, h, 



(1LC 

(AjBis^, 0, 1 



is 0, 1,/V. Hence^ CA^ C t A 



B C v B t C meet in A 2 , viz. 



AB p AjB 



B 2 , „ 
C 2 , " 



~ h 9, 9* h 
/, ~hf h 

/> 9- -f'J 



h 
~9 



0, -K g 

0, -/ 
/» o 



= 0. Therefore A A 2 , B B 2 , C C 2 intersect in a point — say P.,. 

P 2 is /, g, h. 
P x and P 2 may he called inverse or reciprocal points. 



BCis 
B 1 C 1 is 
B 2 C 2 is 



Theorem 4. 
l, o, o. 

l-/ 2 , h+fg, g + hf 

s*(W f ), fQ>+f9), f(9+¥)- 

B C, B 1 C X , B 2 C intersect in % v 

* CA, C^, C 2 A 2 „ iS r 

AB, A^, A 2 B 2 „ © r 



0. Therefore 



By symmetry. 



SEVENTY-TWO CONSECUTIVE PROPOSITIONS IN TRANSVERSALS. 

Theorem 5. 



41 



A X A 2 is 
B, B 2 is 
C 1 C 2 is 



9 2 -h 2 , 
-<7(W 2 ), 



-Mi-/), 

A 2 -/ 2 , 

/(i-V), 



0(1 -A 2 ) 

-/(1-A 2 ) 



0. Therefore ; — 



AjAjj, BjBg, C X C 2 intersect in a point, — say P 3 , viz.,f—gh, g — hf, h—fg. 



Theorem 6. 



P, is 
P 2 is 
P 3 is 



gK ¥, fg- 

f, g> h - 

f-gh, g-hf, h-fg 



= 0. Therefore P l( P 2 , P 3 range in a straight line. 
P^P, is/(/-A 2 ), g (A 2 -/ 2 ), h (/ 2 -<7 2 ). 



A X B, B C meet in a 2 , viz., 
BjCCA „ i$ 2 , „ 
C X A, AB „ e 2 , „ 



0, 1, -/ 
■9, °, 1 

1, -h, 



Theorem 7. 

( CjA, B C meet in a 3 viz., 



Hence ; — 



35 2 © 2 
© 2 ^ 2 



/*, 1, gh 
¥, /, i 

i, fg, g 



Also ; — 



^ 3 ®„ meet in A 3 , viz., 

B 3' 

C. 



© 2 a 2 , € 3 a 3 
a 2 2S 2 , a 3 3S 3 



)5 

'3' " 



Farther ; — 



iS 2 3 

® 2 a 3 




Hence ;- 



Now; — 



3S 2 ® 3 , 23 3 © 2 meet in A 4 , viz., 

® 2 a 3 , e 3 a 2 „ b 4 , 
a 2 B 3 , a 3 33 2 „ a 



'4, » 



Also^ A X B, CA „ 33, 



( B X C, A B 



©, 




*'3* J '3 



is r #, ^, l, ^ 

is -j 1, h, hf, I ; 
is Ifg, 1, /, J 



' 1-flW, A(^-l), ^(A 2 -l) 

A(/ 2 -l), 1-A 2 / 2 , /(^ 2 -l) 

<7(/ 2 -i), /(^ 2 -i) s i-/V 



33 3 © 2 



M/ 2 -i), 

0(/ 2 -l), 



f, hf, h I ; 

/. g> fg J 

h(g*-l), g(h?-\) 

p-h\ /(A 2 -l) 



A being 
A 



1, 0, 

1-gW, h(g*-l), <?(A 2 -1) 

fc 2 -/, M? 2 -i), ?(^ 2 -i) 



A A 3 A 4 is a straight line. 
B B 3 B 4 „ ,, 
C C 3 C 4 „ ,, 



0. Therefore ; — 



AA 3 A t is 
B B 3 B 4 is 
C C 3 C 4 is 



Theorem 8. 

0, <7(1 -A 2 ), -A(l-V) 

-/(1-A 2 ), 0, A(l-/ 2 ) 

f{\-g% -g(l-f 2 ), 



A A 3 A 4 , B B 3 B 4 , CC 3 C 4 meet in a point P 4 , viz., 



VOL. XXIV. PART I. 



0. Therefore ;- 



l_/2 \_ g 2 l _ h 2 

~c > ' 1 ' 

f 9 h 



M 



42 



REV. HUGH MARTIN ON TRILINEAR CO-ORDINATES 



Theorem 9. 



A, is 
A 2 is 
A 3 is 



-1, 

-gh 

1-gW, 



9> 

h(g 2 - 



9 
h 

1), 9(^-1) 



0. Therefore ; — 



A,A 2 A 3 is a straight line. 

B 1 B 2 B 3 » » 

^1 ^2^3 >> " 



Theorem 10. 



B 3 C 3 is 1+fgK h+fg, g + hf; meeting B C in 3, 
C 3 A 3 is h+fg, l+fgh, f+gh; „ CA „ 33, 

A3B3 is g + hf, f+gh, l+fgh; „ AB „ 0, 



Therefore ;- 



BC, B,C„ B 2 C 2 , B3C3 meet in £,. 
CA.CA.CA, C3A3 „ 33,. 
AB, A,B„ A 2 B 2 , A3B3 „ <£,. 



Theorem 11. 



B C, B 4 C 4 meet in & 4 , viz., 
CA, C 4 A 4 „ 33 4 , „ 



AB, A 4 B 4 



0, (f-gh) . (h+fg), -(f+gh).(g-hf) 

■(g + hf).(h-fg), 0, (g-hf).(f+gh) 

{h-fg) .{g+hf), -(h+fg).{f-gh), o 



Therefore Sl 4 33 4 © 4 is a straight line, viz., 



1 



(? + */)• (* -/SO' {h+fg).{f-ghV (f+gh).(g-hfy 



Theorem 12. 



BjC, A,B meet in A 5 , viz., j" — h, 

C 5> » 



C X A, B,C 
A,B, C,A 



h, 1, cjA) 

!» /</» -g J 



BC,, CA, meet in A 6 , viz., ( —g, gh, 1 ] 
CA„ AB, „ B c , „ 1 1, -A, hf 
AB„ BC, „ C 6 , „ ( fg, 1, -/ J 



A 5 A 6 , B C meet in & 5 , viz,, 



B 5 B 6 ,CA 
C s C fi ,AB 



*"5> " 



0, ^(1-A 2 ), -A(l-^) 

-/(i-n o, mi-/ 2 ) 

/(i-/). -?(i-/ 2 ), o 



0. Therefore ;- 



is a straight line, viz., 



1-/2 1_^2 1 _ A 5 

"7" T~' "A- 



Theorem 13. 



B C is 
B 5 C 6 is 
B 6 C 5 is 



1, 
/ f -l. 

%(W 2 ), 



0, 

g+hf 



o 

M+fg) 
h+fg 



= 0. Therefore ;— 



B C, B 5 C 6 , B 6 C 5 meet in a point : 
CA, C 5 A C , C 6 A 5 ,, ,, 



AB, A 5 B 6 , A 6 B 5 



©. 



SEVENTY-TWO CONSECUTIVE PROPOSITIONS IN TRANSVERSALS. 

Theorem 14. 



43 



fl is 


o, 


h+fg, 


-(9+V) 


« 1S 


-( h +M 


o, 


f+gh 


6 is 


9 + V> 


-(f+gh), 






= 0. Therefore ;— 



a 6 23 6 ® 6 is a straight line, viz., f+gh, g + hf, h+fg. 
^IjBj^ and & 6 i3 e @ 6 are inverse or reciprocal lines. 



t'X 



is 



is 



Theorem 15. 

(h+fg) -(f+gh), (g+hf). (h+fg), (f+ghf 

(g+¥)\ (f+gh).(g+¥), (h+fg). (f+gh) 
(f+gh).(g+¥), (h+fgf, (g+¥).(h+f g ) 



and meets B C in & 7 
CAiniS 7 
A B in ©„ 



o, (f+gh) 2 , 

-(h+fg). (f+gh), o, 

(h+fgf, -(f+gh).(g+hf), 



(g+¥).(h+f g ) 
(g+¥f 





= 0. Therefore ;- 



l 7 !5A ^ a straight line, viz., f±& ^-, ^±g- 



riSg^ meeting BC in 
Similarly, ^ @ 6 ^ „ 



f i 



*6*"i 



C A in 33 8 
A B in O 



Theorem 16. 



8 ® 8 is a straight line, viz., 



h+fg f+gh g + hf 
g + hf h+fy' f+gh' 



& 7 3S 7 ® 7 and H 8 H$ 8 <£ 8 are reciprocal lines. 



Theorem 17. 



AAj is 
B B 5 is 
C C„is 



o, 


g, - h 


1, 


0, hf 


1,- 


-fg, o 



0. Also 



' A A 2 is 
BB 6 is 
C C 5 is 



o, 


h, 


-g 


hf, 


o, 


l 


fg, 


-i, 






= 0. Therefore : — 



A A x , B B 5 , C C 6 meet in a point A 7 viz., fgh, h, g. 



BB X> CC 5) AA 6 
CC 1; AA 5 ,BB 6 



B, 



h, fgh, f. 

g, /> fgh- 



Theorem 18. 



AA 2 , BBg, C C 5 meet in a point A 8 viz., I, fg, hf. 
BB„, CCA A. „ „ B 8 „ fg, 1, gh. 

C 8 „ hf, gh, 1. 



BB 2 , CC 6 ,AA 5 
CC 2 , AA 6 , BB 5 



But instead of continuing the manipulation, we shall gather up these results, 
and continue the series of propositions. 



44 REV. HUGH MARTIN ON TRILINEAR CO-ORDINATES I 

Theorem I. 

A A v B B p C C, intersect, in a point, P r 

Theorem II. 

Let B C, B 1 C 1 meet in S x j 

C A, C 1 A l „ B, J . Then ;—^ l B 1 € 1 is a straight line. 
AB, A^ „ ©J 



Theorem III. 



C v B t C meet in A 2 ") 

A C. A „ B I. Then ;— A A 2 , B B 2 , C C 2 meet in a point, P„ 

B p A,B „ C 2 J 



Let B C v B t C meet in A 
C 
A 



Pj and P 2 are reciprocal points. 

Theorem IV. 

B C, B 1 C p B 2 C 2 intersect in a point, and that point is ^ 
C A, CjAp C 2 A 2 „ „ )} J3 1 

A B, A^j, A 2 B 2 „ „ „ e t 

Theorem V. 

A X A 2 , BjBj, CjC 2 intersect in a point, P 3 . 

Theorem VI. 

P X P 2 P 3 is a straight line. 

Theorem VII. 

Let A X B, B C meet in & 2 1 And let Cj A, B C meet in & 3 1 

BjC, CA „ 33j; A 1 B, CA „ B 3 

C A, AB „ ©J BjC, AB „ ®J 

Also let B 2 ffi 2 , B 3 e 3 meet in A 3 \ And let 33 2 © 3 , B 3 # 2 meet in A 4 
© 2 2l 2 , © 3 ® 3 „ B 3 l; 0^, e 3 a 2 „ B 4 

a 2 i3 2 , a 3 B 3 „ c 3 J a 2 B 3 , <a 3 B 2 „ c 4 . 

Then, — A A 3 A 4 is a straight line. 

BB 3 B 4 » » 

C C 3 C 4 „ „ 

Theorem VIII. 

A A 3 A 4 , B B 3 B 4 , C C 3 C 4 meet in a point, P 4 . 

Theorem IX. 

AjA 2 A 3 is a straight line. 

B 1 B 2 B 3 « » 

C 1 C 2 C 3 » » 



SEVENTY-TWO CONSECUTIVE PROPOSITIONS IN TRANSVERSALS. 45 

Theorem X. 

BC, B^, B 2 C„ B 3 C 3 all meet in & r 
CA, C X A 15 C 2 A 2 ; C3A3 „ 33 r 

AB, A^ v A 2 B 2 , A3B3 „ e v 

Theorem ' XI. 

LetB C, B 4 C 4 meet in &A 

C A, C 4 A 4 „ 2S 4 } . Then ;— & 4 1S 4 © 4 is a straight line. 
AB, A 4 B 4 „ ej 

Theorem XII. 

Let B^, A X B meet in A 5 ^ And let B C p C A x meet in A 6 } 

C X A, B X C „ bA;— CA X , A B x „ B 6 \. 

A t B, C X A „ C 5 J AB 15 BC X „ C 6 J 

; B C, A 5 A e 
CA, B 5 B 6 
AB, C 5 C 6 



Also let B C, A 5 A 6 meet in 

C A, B 5 B 6 „ 2Sg }■ . Then ;—& 5 3$ 5 © 5 is a straight line. 



Theorem XIII. 

B C, B 5 C 6 , B 6 C 5 meet in a point, & 6 . 
CA, C 5 A 6) C 6 A 5 „ „ 2S 6 . 
AB, A 5 B 6 , A 6 B 5 „ „ ® 6 . 

Theorem XIV. 

& 6 3S 6 ® 6 is a straight line; reciprocal to ^ X 33 1 @ 1 . 

Theorem XV. 

Let B C, t3 x © 6 meet in % \ 

C A, ©, a 6 „ 33 7 L Then ;— & 7 25 7 @ 7 is a straight line. 
AB, a^e „ ©J 

Theorem XVI. 

Let B C, 33 6 © x meet in & 8 ) 

C A, @ 6 gL „ ®A. Then ;— & 8 B 8 ® 8 is a straight line ; reciprocal to & 7 2S 7 ©» 

ab, a,^ „ ej 

Theorem XVII. 

A A v BB r , C C 6 meet in a point, A 7 . 
BB X , CC 5 J , AA 6 „ „ B 7 . 
CC X , AA 5 , BB 6 „ „ C 7 . 

Theorem XVIII. 

A A 2 , B B 6 , C C 5 meet in a point, A 8 . 
BB 2 , CC 6 , AA 5 „ „ B 8 . 
CC 2 ,AA 6 , BB 5 „ „ C 8 . 

Theorem XIX. 

A 7 A 8 , B 7 B g , C 7 C 8 meet in a point P 5 . 
VOL. XXIV. PART I. N 



46 REV. HUGH MARTIN ON TRILINEAR CO-ORDINATES : 

Theorem XX. 

B C, B 7 C 7 , B g C 8 meet in a point, & 9 . 
CA, C 7 A 7 , C 8 A 8 ,, „ 23 9 . 
AB, A 7 B 7 , A 8 B 8 „ „ ©,. 

Theorem XXI. 

& 9 33 9 (£ 9 is a straight line. 

Theorem XXII. 

B C, A A 2 , AgPj, A 7 P 2 all meet in a point, & 10 . 
CA, BB 2 , B 8 P U B 7 P 2 „ „ 33 10 . 

AB, CC 2 , C 8 P X , C 7 P 2 „ „ © 10 . 

Theorem XXIII. 

A & 9 , A C, A iU 10 , A B is a harmonic pencil. 
B*„ BA, B» 10 , BC „ 

ce 9 , CB, C© 10 , CA „ 

Theorem XXIV. 

B C, A 1 P 2 , A 2 P X meet in a point, & ir 
CA, B^,, B 2 P t „ „ JJ U . 
AB, C 1 P 2 , C.jPj ,, „ ffi 11 . 

Theorem XXV. 

A & n , B 33 n , C dt u intersect in a point, P 6 . 

Theorem XXVI. 

B C, AjAg, A 2 A 7 meet in a point, 3 12 . 
CA, B.Bg, B 2 B 7 „ „ & 12 . 

AB, CjCg, C 2 C 7 „ ,, © 12 . 

Theorem XXVII. 

A & 12 , B 35 12 , C © 12 intersect in a point, Q r 

Theorem XXVIII. 

Let B C, A 7 A 8 meet in & 13 ~J 

CA, B 7 B 8 „ 1S 18 j> ;— Then, A a ig , B B 13 , C© 13 intersect in a point, Q 2 . 

Theorem XXIX. 

— Then, A A 9 , B B 9 , C C 9 intersect in a point, Q 3 . 

Theorem XXX. 

Let AjAg, A 5 A 6 meet in A 10 | 

B X B 2 , B 5 B 6 ., B 10 > ; — Then, A A 10 , B B 10 , C C 10 intersect in a point, Q 4 . 



AB, 


c 7 c 8 


)5 




B 5 B 6» 

C r C r , 

5 6' 

A 5 A 6> 


c 5 c 6 

A 5 A 6 

B 5 B 6 


meet 


in A 9 
B 9 

c 9 



C X C 2 , C 5 C 6 „ c 



10 



SEVENTY-TWO CONSECUTIVE PROPOSITIONS IN TRANSVERSALS. 47 

Theorem XXXI. 

Let B C, A A 7 meet in H And let B C, m n meet in l x \ 

CA, BA 7 „ ml; CA, nl „ rn 1 > . 

AB, CA, „ n) AB, Im „ n x ) 

Then l^m^ is a straight line, as is well known. As it depends entirely on the position of A 7 let 
it be called (p (A 7 ). Then ; — 

<p (A 7 ) is the polar of A 8 to the imaginary conic, a 2 + /5 2 + 'y 2 =0. 
(p (B 7 ) „ B 8 „ 

<p (C 7 ) „ c s „ ,, ,, 

Theorem XXXII. 

(p (A 8 ) is the polar of A 7 to the imaginary conic, a 2 4-/3 2 -J- r y 2 =0. 

<P (B 8 ) „ B 7 „ „ 

9 (C 8 ) „ C 7 „ ,, „ 

Theorem XXXIII. 

(p (P x ) is the polar of P 2 to the imaginary conic, a? +j3 2 + r y 2 = 0. 

(p (."2) )> "1 >) )> ;> 

Theorem XXXIY. 

(p - 1 (&! a x ©J is the pole of & 6 9$ 6 @ 6 to the conic, a 2 + /3 2 + 7 2 = 0. 

0-»(a 6 » e e 6 ) „ «!*!©! „ 
Theorem XXXV. 

(p - 1 (8L U 7 © 7 ) is the pole of & 8 2S 8 ® 8 to the conic, a 2 + /3 2 +7 2 =0. 

0-i(a 8 * 8 © 8 ) „ a 7 ?3 7 e 7 „ 

The principle of reciprocation would introduce here a number of Propositions 
which it is unnecessary to enunciate. 

Theorem XXXVI. 

Let A A v B 7 C 7 meet in l 2 \ And let B C, m^n 2 meet in a x 

BB 1; C 7 A 7 „ mA; CA, n 2 l 2 „ ft 

CC 1S A 7 B 7 „ nj AB, l 2 m 2 „ 7, 

Then ;• — « 1 /3 1 7 1 is a straight line. 

Theorem XXXVII. 

Let A A 2 , B 8 C 8 meet in l z ~\ And let B C, m 3 n 3 meet in a 2 \ 

BB 2 , C 8 A 8 „ m, \; CA, n 3 l 3 „ #, 

CC 2 , A 8 B 8 „ nj AB, Z 3 m 3 „ 7, J 

Then ; — # 2 /3 2 7 2 is a straight line. 

Theorem XXXVIII. 

Let /8 1 7 2 » |5 2 Ti meet m a 3 1 

Ti a 2' 72 a i » & f' — Then, a 3 6 3 y z is a straight line. 
«!&, «2^1 » 7 3 J 



48 REV. HUGH MARTIN ON TRILINEAR CO-ORDINATES : 

Theorem XXXIX. 

Let a x /3 2 , y 1 a 2 meet in a A And let a 8 ft, y 2 a 1 meet in a 

ft 7 8 . gift » ft>; p 9 y v a 2 /5 x n fl 

7i« 2 >ft7 2 » 7 4 J 7 2 «i»ft7i » 7 

A a.a, is a straight line. 
Then;- B ft/3 3 „ „ 

C 7*7 5 

Theorem XL. 

A a 4 a 5 , B /5 4 /3., C 7 4 y 5 meet in a point. 

Theorem XLI. 

Postulating again, similarly as in Theorems XXXVI. and XXXVII.,- 

Let A A 2 , B 7 C 7 meet in L ; and similarly "» 
. , , A _ „ - \ . Then ; — 

Also A Aj, B 8 C 8 ,, ? 3 ; and similarly J 

a \ ft 7i ^ s a straight line. 

Theorem XLII. 

a 2 ft y 2 is a straight line. 

Theorem XLIII. 

a 3 ft 73 * s a straight line. 

Theorem XLIV. 

A a 4 a 5 is a straight line. 
Bftft „ „ 
c 7 4 7 5 



>) )! 



Theorem XLV. 

A a 4 a 5 , B /3 4 (3 5 , C Y 4 y 5 meet in a point. 

Theorem XLVI. 

Let a y a 2 , a 1 a 2 meet in a 6 

Aft, ft ft „ ft Then;- 

7i7 3 . 7i7 2 » 7 a 

A a 6 , Bj9 6 , C7 6 ; A 7 A S , B 7 B 8 , C 7 C 8 all intersect in P 5 . 

Let P 3 Q 3 and P 6 Q 1 meet in Q 5 ; and let P 5 Q 5 and P 4 Q 4 meet in Q 6 . 
Then the points P 15 P 2 , P 8 , P 4 , P 5 , P 6 ; Q 1; Q 2) Q g> Q 4> Q., Q g have very remarkable relations. 

Theorem XLVII. 

Pj, P 2 , P 3 , P 4 , P 5 , P 6 all range in a straight line. 



SEVENTY-TWO CONSECUTIVE PROPOSITIONS IN TRANSVERSALS. 49 

Theorem XLVIII. 

Q X Q 4 and Q 3 Q. intersect in P 3 . 

Theorem XLIX. 

Q 2 Q 5 and Q 4 Q 6 intersect in P 4 . 

Theorem L. 

QjQg and P X P 2 intersect in P 5 . 

Theorem LI. 

QjQ. and Q 3 Q 4 intersect in P 6 . 

Theorem LII. 

P^Qg and P 5 Q 4 intersect in Q 2 . 

V 

Theorem LIII. 

P^, Q X Q 2 , Q 3 Q 6 intersect in a point. 

Theorem LIV. 

Q X Q 3 , QA, Q 2 Qe intersect in a pomt,— say JT. 

Theorem LV. 

Let CLQ, and Q.P. meet in S x \ . And let Q 3 Q 5 and Q 4 Q 6 meet in S 3 \ T h en •— 
ofc, and Q> 8 " „ S 2 j' QxQ.andQA „ S 4 j 

S^ X is a straight line. 

Theorem LVI. 

S3S4 j? is a straight line. 

Theorem LVII. 

Let P^Q, and P 2 Q 3 meet in R x 1 . And let P X Q 4 and P 2 Q 5 meet in R 3 "1 Then ._ 
P^andP^ „ R 2 J' P^andP^ „ R 4 J 

R X R 2 Jf is a straight line. 

Theorem LVIII. 

R 3 R 4 JP is a straight line. 
VOL. XXIV. PART I. ° 



50 REV. HUGH MARTIN ON TRILINEAR CO-ORDINATES : 

Theorem LIX. 

Let P X Q 6 and P 2 Q 2 meet in TJ 1 "1 T , 

P^andP^Q, „ U 2 ) inen; ~ 

UjUg lr is a straight line. 

Theorem LX. 

V x V a ; R^, R 3 R 4 ; S X S 2 . S 3 S 4 ; Q^, Q 4 Q., Q 2 Q ; all intersect in P. 

Theorem LXI. 

AT is the pole of P^PgP^.Pg to the imaginary conic, a 2 + fi 2 + y 2 = 0. 

Theorem LXII. 

The lines AA X , BB 1? CC X ; AA 2 , BB 2 , CC 2 cut the sides of the triangle ABC 
in six points which lie in the conic ; — 

*+p+i>- (i+l)f>y- C+{)7«- (£+$)•*-«■ 

For the six points are inverse or reciprocal points. Substituting the co-ordinates 
of five of them (the third of the second set being omitted) in the general equation 
of the second degree, and eliminating the arbitrary constants, gives the conic as 
above. To substitute the co-ordinates of five of the points, omitting now the 
third of the Jirst set, amounts evidently to inverting the separate terms in the 
constants of the above equation ; and as this leaves it unaltered, the proof of the 
theorem is obvious. 

Theorem LXIII. 

The lines AA 5 , BB 5 , CC 5 ; AA e , BB 6 , CC 6 cut the sides of the triangle ABC in 
six points which lie in the conic ; — 

«. + * + 7 .- (* + i)07- (''/+^)7«-(/?+!)«£ = 0. 
Theorem LXIV. 

The points 8^3$^ ; ^ 2 15 2 € , 2 lie in the conic;— 

Theorem LXV. 

If the point P x move in a straight line, the line (P x ) will always touch a 
conic which touches the three sides of the triangle ABC. 



SEVENTY-TWO CONSECUTIVE PROPOSITIONS IN TRANSVERSALS. 51 

Let the equation of the line in which P x moves be la + m(3 + ny = ; or sub- 
stituting the co-ordinates of P x now supposed variable (see Theorem 1), 

/ 9 h 
0(P x )is fa + g(3 + hy = = u . . . . . (2). 

Now h may be considered as constant, since it is the ratios only that are con- 
cerned. Take /as the independent variable, then g varies with /by (1) ; and by 
the theory of envelopes we have 

|=»= ($) + (!)■ I < 3 >- 

Elimination gives =i= (la)* ± (m/3)* rb (ny)* = ; — 

the equation of a conic touching the sides of the triangle of reference. — Q. E. D. 

Theorem LXVI. 

Let lines be drawn from the angles of a triangle through any two points and 
terminating in the opposite sides ; by joining the extremities of each set of lines 
so drawn, two other triangles will be formed. The three lines joining the inter- 
sections of corresponding sides of these two triangles with the corresponding 
angle of the original triangle meet in a point. 

If the co-ordinates of the two assumed points be a, 5 X c x and a 2 b 2 c 2 those of 
the third point are 



b v b 2 

C V C 2 


, h b 2 


C V C 2 

a v a 2 


> C l G 2 


Cv-. a Cw-j 

b vh 



Let this point be called the anapole of the two assumed points. 

Theorem LXVII. 

The anapoles of A 7 , A 8 ; of B 7 , P> 8 ; and of C 7 , C 8 are in a straight line, — say #\i IBi ©i 

Theorem LXVIII. 

The straight line joining the anapoles of P x , A 8 and P 2 , A 7 passes through A ; cutting BC (say) in $\ 2 - 

» » >> "l> "8 " 2' ""7 » ■"» » C" » ©2' 

» » » Pi> C 8 „ P 2 , C r „ C; „ AB „ (g 2 . 

^2 ©2 ©2 is a straight line, identical with ^.B 5 © 5 of Theorem XII. 

Theorem LXIX. 

The lines $\i ©i ©n ^ 2 ^ 2 © 2 intersect in the anapole of P x , P 2 , which is also the 
pole of the line P x P 2 to the imaginary conic, a 2 + /3 2 + y 2 = 0. So that the 



52 KEV. HUGH MARTIN ON TRILINEAR CO-ORDINATES. 

anapole of inverse points is the pole of the line joining them — to the same 
imaginary conic. 

Theorem LXX. 

If one of two points remain fixed and the other move in any manner what- 
ever, the locus of the anapoles is a straight line. 

Theorem LXXL 

If two points move away from each other along a straight line with uniform 
velocities, their anapole will describe a conic section ; and if the uniform veloci- 
ties be equal, a straight line. 

Theorem LXXII. 

The anapole of any two points in a conic section passing through the angles 
of the triangle of reference is invariable, and its co-ordinates are proportional to 
the sides of the triangle. 



( 53 ) 



VI.— Note on Confocal Conic Sections. By H. P. Talbot, Esq. 

(Read 17th April 1865.) 

A short paper of mine on Fagnani's theorem, and on Confocal Conic Sections, 
was inserted in the twenty-third volume of the Transactions of the Royal Society. 
Some of the conclusions of that paper can, however, be obtained more simply, as 
I will now proceed to show. 

I will, in the first place, resume the problem— 
" To find the intersection of a confocal ellipse and hyperbola." 
Since the curves have the same foci, and therefore the same centre, let the 
distance between the centre and focus be called unity, since it is the same for 
both curves. Let a, b, be the axes of the ellipse, A, B, those of the hyperbola 
Then we have 1 = a 2 — b 2 = A 2 + B 2 , which equation expresses the condition of 
confocality. 

The equation of the ellipse will be -g- + yg- = 1, and that of the hyperbola 



2 2 

-^2 - ^2 = 1. But at the point of intersection x and y are the same for both 

curves. We have therefore two equations from which to determine two unknown 
quantities. The result is one of unexpected simplicity. (See Vol. XXIII. p. 295.) 

x = Aa , y = ~Bb . 

The theory of the Conic Sections has been so much studied, that I can scarcely 
suppose that a result of such extreme simplicity, and so fruitful in remarkable 
results, should not have occurred to some previous mathematician. I have no 
had the opportunity of late of consulting many treatises on the Conic Sections, 
but in those which I have examined I have not found this theorem. 

I will not here repeat the proof which I gave of it in my former paper, since 
it suffices to show that these values of x and y satisfy both the given equations. 

In fact, if we put x = Aa and y = B5, the equation -^- + ^ = l becomes 

A 2 + B 2 = 1, which is true, and the equation -^ - ^ = * becomes of —b 2 = 1, 

which is also true. 

This fundamental theorem being thus established, I shall proceed to show how 
easily the theorem of page 296 follows from it, viz., 

VOL. XXIV. PART I. P 



54 MR TALBOT ON CONFOCAL CONIC SECTIONS. 

" If two ellipses and two hyperbolas have all of them the same centre and 
foci, and therefore intersect in four points, forming a curvilinear quadrilateral, the 
diagonals of this quadrilateral are equal." 

There will, of course, be a similar quadrilateral on the other side of the axis 
major. 

In proof of this theorem, it is sufficient to calculate the value of one diagonal, 
for since that is found to be a symmetrical function of the four greater axes of the 
given curves, the second diagonal has necessarily the same value. 

This may be shown thus (Vol. XXIII., fig. 15, p. 296). Adopting the former 
notation, the square of one of the diagonals, or D 2 = (x — xf + (y — y) 2 

where 

x = Aa y = B/> 

x = Aa y = Bb 
... D 2 = (a? + y 2 ) + (f + f) - 2- - 2yy 

But xx — kkaa, which is a symmetrical quantity, being the product of the four 

major axes :— and yy = BBbb is a symmetrical also, being the product of the four 

minor axes. 

Therefore it remains to show that (x 2 + y 2 ) + (x 2 + y 2 ) is a symmetrical 

quantity. 

Now 

x 2 + y 2 = A 2 a 2 + B 2 b 2 

but 

B 2 6-' = (1 - A 2 ) (a 2 - 1) = - 1 + (A 2 + a 2 ) - AV 
.-. x 2 + y 2 = (A 2 + a 2 ) - 1 . 
And similarly 

x 2 + y 2 = {A 2 + a 2 ) - 1 

.-. (x 2 + y 2 ) +(x 2 + f) = (A 2 + A 2 + a 2 + a 2 ) - 2 

which being a symmetrical quantity, the truth of the theorem in question is 
demonstrated. 

From this theorem many others may be deduced ; some of which I have given 
in my first memoir. The following elegant theorem was communicated to me by 
Charles H. Talbot, Esq. 

" If the direction of one of the diagonals passes through the focus, that of the 
other diagonal passes through the other focus." 

Demonstration. — First take the general case in which neither diagonal passes 
through a focus (see fig. 1). Let the diagonals be PP', QQ'; join HP, HP' and 
SQ, SQ';— then I say that HP'— HP = SQ , -SQ. 



MR TALBOT ON CONFOCAL CONIC SECTIONS. 



55 



For, by a theorem in my former paper (p. 295), if two confocals intersect, the 
focal distance of their intersection equals the distance between their vertices. 




A A 



V' V H 



B B 



Fig. 1. 



Thus, if AP be the ellipse, and VP the hyperbola (fig. 2), AB the major axis, 




Fig. 2. 

S, H, the foci ; SP will be equal to AV, and HP to BV. 
Therefore in fig. 1 we have 

HF=VB, HP=VB, SQ-=A'V, SQ=AV 

.-. HP'-HP=VB-VB=VV + BB' 

and SQ'-SQ=A'V-AV=VV + AA' 

.-. (since AA'=BB') HP'-HP=SQ'-SQ. 

This, of itself, is a curious theorem. The other follows immediately from it. 

For, in the particular case, where HPP is a straight line, HP'— HP is the 
diagonal PP', which is always equal to the diagonal QQ'. 

Therefore, in this case, SQ'— SQ = QQ', and therefore SQQ' is a straight line, 
which was to be proved. 

Another theorem which I have found concerning these quadrilaterals is the 
following. 

" If one of the diagonals is a tangent to the inner ellipse, the other diagonal 
is so likewise." 

I omit, for the present, the demonstration of this, which is not difficult. 

I deduced from Graves's theorem in my former paper the remarkable conse- 
quence, that if a triangle or other polygon is inscribed to the one, and circum- 



56 



MR TALBOT ON CONFOCAL CONIC SECTIONS. 



scribed to the other, of two confocal ellipses, its perimeter is constant, at what- 
ever point of the exterior ellipse it is supposed to commence. 

But the truth of this can be shown without any reference to Graves's theorem, 
from the simple consideration that two consecutive sides of the triangle make 
equal angles with the periphery of the exterior ellipse. Hence if the point of 
departure, or vertex of the triangle, suffers a very small displacement, the three 
sides increase or diminish at one end by three small quantities 8, 8', 8" (generally 
speaking all different). 

Let us suppose this to occur at the right extremity of each of the three lines, 
then it is evident that the increments (or decrements as the case may be) which 
occur at their left extremities will be — 8", —8,-8' respectively (because each 
side gains at one end what the following side loses there). Therefore the total 
increase of the perimeter = (8 — 8") + {8'— 8) + (8"— 8') = 0. A much more 
general theorem can be proved in the same way. " If a triangle cirumscribes an 
ellipse, and its three angles rest upon the peripheries of three other ellipses (all 
four having the same foci), the perimeter of the triangle is constant." 

I find that Chasles has given this theorem (although without proof) in his 
memoir, which I have already quoted (see my last paper, p. 287). The same is 
true of polygons of n angles resting upon n confocal ellipses. 

I will conclude this short note by giving a curious property of the circle, com- 
municated to me by C. H. Talbot, Esq. 

" If three concentric circles (fig. 3) are described from any centre S, with 




■H 



radii m, m + h, m + 2h. And if three other concentric circles intersecting them 
are described from any other centre H, with radii n, n + k, n + 2h [m, n, h having 



MR TALBOT ON CONFOCAL CONIC SECTIONS. 57 

any values] ; then the chord of PQ', the middle arc of one series, equals the 
chord of P'Q, the middle arc of the other series."* 

Demonstration.— In each series of circles the radii have a common difference 
h, which may be called the interval between them. P and P' are two points in 
the same ellipse of which S, H, are the foci, because in passing from P to 
P', SP increases by one interval h, and HP diminishes by the same, therefore 
SP + HP remains constant. 

By similar reasoning Q and Q' are two points in a second ellipse having same 
foci. Moreover P and Q are two points in a hyperbola of which S, H, are foci ; 
because in passing from P to Q, both HP and SP increase by one interval h y and 
therefore HP — SP remains constant, and equal to HQ — SQ. 

By similar reasoning P' and Q' are two points in a second hyperbola having 
same foci. Therefore P, P', Q, Q' are the intersections of two ellipses and two 
hyperbolas, all confocal. Therefore the diagonals PQ', P'Q are equal to each 
other.— Q.E.D. 

This property of the circle should be readily demonstrable by Euclid's 
Elements ; a simple geometrical demonstration is, however, at present a desi- 
deratum. 

* The second or middle circle of one series must be understood to be limited by the first and 
third circles of the other. 



VOL. XXIV. PART I. Q 



( 59 ) 



VII. — On the Motion of a Heavy Body along the Circumference of a Circle. By 

Edward Sang, Esq. 

(Read 20th March 1865.) 

In the year 1861 I laid before the Royal Society of Edinburgh a theorem con- 
cerning the time of descent in a circular arc, by help of which that time can be 
computed with great ease and rapidity. A concise statement of it is printed in 
the fourth volume of the Society's Proceedings at page 419. 

The theorem in question was arrived at by the comparison of two formulae, 
the one being the common series and the other an expression given in the "Edin- 
burgh Philosophical Magazine" for November 1828, by a writer under the signa- 
ture J. W. L. Each of these series is reached by a long train of transformations, 
developments, and integrations, which require great familiarity with the most 
advanced branches of the infinitesimal calculus ; yet the theorem which results 
from their comparison has an aspect of extreme simplicity, and seems as if surely 
it might be attained to by a much shorter and less rugged road. For that reason 
I did not, at the time, give an account of the manner in which it was arrived at, 
intending to seek out a better proof. On comparing it with what is known in 
the theory of elliptic functions, its resemblance to the beautiful theorem of Halle 
became obvious; but then the coefficients in Halle's formulae are necessarily 
less than unit, whereas for this theorem they are required to be greater than unit. 

The search after the mutual relations of the two theorems has led me to the 
discovery of a few simple propositions which involve only the very first principles 
of the calculus, and the well-known law that the square of the velocity which 
a heavy body acquires in descending along a curve is proportional to the vertical 
distance, and to the intensity of gravitation jointly ; and which, yet, contain the 
whole theory of motion in a circle whether that motion be oscillatory or con- 
tinuous. I am thus enabled to present this hitherto intricate theory in a form 
which renders it intelligible to junior students of mechanical science. 

By a well-known method of extension, the doctrine of the motion of a heavy 
physical point along the circumference of a circle can be made to include that of 
the rotation of any mass of matter on an axis not passing through its centre of 
gravity, whether that axis be horizontal or be inclined ; hence, in the following 
investigation, I may confine my attention to the motion of a physical point in the 
circumference of a circle placed vertically. 

2. Let N be the nadir and Z the zenith point of a circle, along the circum- 
ference of which a minute heavy body is free to move. If that body be projected 

VOL. XXIV. PART I. R 



60 



MR EDWARD SANG ON THE MOTION OF A HEAVY BODY 




from N with some given velocity V, it will ascend along the circumference, losing 

velocity as it rises. When the initial velocity 
exceeds that which is due to a descent along the 
diameter ZN, the body will rise to the zenith- 
point Z, and will proceed onwards to descend 
along the other semicircumference ; after that 
it will continue (all resistance being supposed 
away) to repeat revolution after revolution. 
But when the initial velocity is less than that 
which is due to a descent along ZN, the heavy 
body will have lost the whole of its velocity at 
some point below Z, from that point it will de- 
scend again to N, pass to the other side, on 
which it will reach to the same height, and 
thence descending it will continue to oscillate 
as in the familiar example of a pendulum. 
There are thus two distinct cases of circular motion, viz., the continuous and the 
oscillatory. 

3. These two cases may be connected in the following manner : — 
Let us suppose that a heavy body a, has been projected at N, with a velocity 
due to its descent from some point A beyond Z, and that it has now reached to the 
point marked a. Having drawn the horizontal line aG, we see that its velocity 
at the point a is that which is due to a fall through the distance AG ; so that if 
we put V A for the initial velocity, and v a for the velocity at the point a, we 
must have the proportion 

Va 2 : v a 2 : : NA : AG : : NZ . NA : NZ . AG 
: : NZ . NA : NZ . NA-NZ . NG . 

Through Z draw the horizontal line ZE, and make it a mean proportional be- 
tween NZ and ZA ; join NE, EA, then the trigons NZE, NEA are similar, so that 
NE is a mean proportional between NZ and NA, wherefore the above analogy 
may be written,— 



V A * 



2 : :NE 2 : NE--Na 2 



4. F being the intersection of NE with the circumference of the circle, draw 
FB horizontally, then the five lines NA, NE. NZ, NF, and NB, are in continued 
proportion ; so that NA : NZ : : NZ : NB. 

If a second body j3 be projected from N, with a velocity due to a descent from 
B, it will rise along the curve only to the point F, its velocity there being entirely 
exhausted. The greatest distance, then, which (3 can reach from N, viz., NF, is 
to the greatest distance to which a can attain, viz., NZ, in the ratio of NE to NA. 
Let us take an intermediate point (3 to correspond with a, by making Na : N/3 



ALONG THE CIRCUMFERENCE OF A CIRCLE. 61 

: : NA : NE : : NE : NZ : : &c. ; and seek the ratio of the two velocities, viz., of a 
at the point a, and of (3 at the point (3. 

5. Putting V B for the initial velocity of (3, and vp for its velocity at the point (3 
we have, — 







V B 2 : Vj3 2 : : BN : BH : : BN : BN-NH 






: : NZ . BN : NZ . BN-NZ . NH 






::NF 2 : NF 2 -N/3 2 . 


But we have also 








V A 2 : V 2 B : : NE 2 : NF 2 , 


wherefore 




v 2 • v „* : : NE 2 -Na 2 : NF 2 -NB 2 

a • a 


Now, from our 


construction, 






NE 2 : NZ 2 : : N« 2 : N/3 2 


wherefore 




NE 2 : NZ 2 : : NE 2 -N« 2 : NZ 2 -N/3 2 


but 




NZ 2 - N/3 2 = Z/3 2 , 


wherefore 




NE 2 -Na 2 : NE 2 : : Z/3 2 : NZ 2 


and similarly 




NE 2 : NA 2 : : NF 2 -N/3 2 : NZ 2 -Na 2 ; 


or, 







NE 2 : NF 2 -N/3 2 : : NA 2 : Za 2 . 
Compounding these ratios we obtain, — 

whence 

NE 2 -N« 2 : NF 2 -N/3 2 : : NA 2 . Z/3 2 : NZ 2 . Za 2 , 
v a . Vp : : NA . Z/3 : NZ . Z« . 

6. Let us now suppose that the body a moves through an exceedingly minute 
distance, represented by aa, and let us make the proximate chord N/3', in the 
same ratio to Na' as before ; then, since N« may be held equal to Na and N& to 
N/3, we have aa' : b(3 : : Na : N/3. 

The minute trigons aaa and b(3(3f are similar, respectively, to aNZ and /3NZ, 

wherefore 

aa' : aa! : : NZ : Za 

6/3' : jSjS' : : Z/3 : NZ . 

By compounding these three ratios we obtain 

aa' : /3/3' : : Na . Z/3 : N/3 . Za 
: : NZ . Z/3 : NF . Za . 

7. On comparing the lengths of the arcs aa' and /3/3', and also the velocities 
with which they are passed over, we find that the minute intervals of time are in 
the ratio 

NZ NF 
time in aa' : time in /3/3' : : r— - : z—z - : : NZ : NE . 

NA NZ 



62 MR EDWARD SANG ON THE MOTION OF A HEAVY BODY 

Now, if we suppose that the semicircumference NaZ is divided into a multitude of 
minute portions, of which aa may be taken as one ; and if we divide the arc N/3F 
into as many corresponding portions by making the chords N/3 always to the 
chords Na in the constant ratio NZ to NE ; the time of describing each element 
aa of the semicircumference NZ is to that of describing the corresponding 
element f3(3' of the arc NF in the constant ratio NZ to NE ; and, consequently, 
the time of describing any portion as Na must be to that of the describing the 
corresponding portion NS in the same ratio ; and so also must be the periodic 
times of the two motions. 

Hence, if we can discover the law of the motion in the arc NF, we shall be 
able thence to deduce the law of the continuous motion due to the velocity 
obtained by descent from the point A ; and contrariwise. 

For the sake of convenience, we shall call these two motions conjugate to 
each other. 

8. It will conduce greatly to the clearness of our subsequent investigations to 
introduce here another consideration. The time of describing the arc NF is 
greater than that of describing the conjugate arc NZ in the ratio of NZ to NF; 
the oscillatory motion will thus fall behind the continuous motion. Now, if we 
were to suppose that the body (3 is acted on by gravitation of an intensity greater 
than that which acts on a in the ratio duplicate of the ratio of the actual periodic 
times, the two motions would be rendered alike. 

We shall then suppose that the gravitation acting on a, which we may desig- 
nate by G„, is proportional to NZ, while the intensity of the gravitation acting on 
/3, appropriately denoted by G^, is proportional to NA. And, as we have to do 
with the subduplicate of the ratio of these intensities, we shall, for the sake of 
additional convenience, put 

G« = NZ . NZ ; G^ = NZ . NA . 

9. The height from which a body has fallen being denoted by h, and the in- 
tensity of gravitation being G, the velocity acquired is, according to the well- 
known law of motion, proportional to V{Gh) ; we shall, therefore, put the general 
formula for that velocity thus : — 

v = J(G . NZ . h) . 

10. On inserting the above value of G a in this general formula, and at the 
same time making h = AG = NA — NG we have 

v a = J {NZ . NZ . NZ (NA - NG)} = NZ . V(NE 2 - Na 2 ) . 
And similarly for the body /3 

vp = J {NZ . NA . NZ (NB - NH)[ = NE . J(NF 2 - N/3 2 ) . 



ALONG THE CIRCUMFERENCE OF A CIRCLE. 



63 



But since 





NE : NZ : : NZ : 


NF : : Na : N/3 




NZ . V(NE 2 - Na 2 ) = NE . 


^(NZ 2 - N/3 2 ) = NE . Z/3 , 


and 


NE . ^(NF 2 - N/3 2 ) = NZ 


V(NZ 2 - Na 2 ) = NZ . Za 


wherefore 








v a = NE.Z/3; 


Vq — NZ . Za . 



Hence, under this supposition of two distinct intensities of gravitation, we 
have 

v a : vp : : NE . Z/3 : NZ . Za , 

but we have shown in Article 6 that the minute distance aa is to the correspond- 
ing distance /3/3' in the very same ratio, wherefore the time in which the body a 
describes the distance aa is now equal to that in which j3 describes the distance 
/3/3'. And consequently if a and /3 start at the same instant from N, they will 
reach the points a and (3 simultaneously; and just when a has reached the 
highest point Z, /3 will have reached its highest point F ; so that the periodic 
times of the two conjugate motions have been made alike. 

11. In the figure 1 hitherto referred to, the points a and (3 have been placed 
on opposite sides of the diameter NZ for the sake of perspicuity. We shall now, 
in figure 2, suppose that they are both projected in the same direction from N 
and at the same instant, so that when a has reached the point a, /3 has reached /3. 
Proceeding onwards, when a comes to Z, (3 
arrives at F, the velocity of a being then that 
which is due to a fall from A to Z, and the 
velocity of /3 being zero. Subsequently, while 
a returns to N along the other semicircum- 
ference, (3 returns to N by retracing its previous 
path FN. In this way both bodies arrive at N 
at the same instant, but moving in opposite 
directions. While a, for the second time, de- 
scribes the entire circumference of the circle, (3 
ascends to L and thence returns to N at the 
same instant that a reaches that point. The 
two bodies are now moving in the same direc- 
tion as at first, and these phases, all resistance 
being set aside, are again and again reproduced. 

12. Let us now imagine that the arc a/3 is 
continually bisected in 7, and let us trace the motion of this middle point. 

When a has reached Z and (3 has come to F, the point 7 must be at M the 
middle of the arc FZ : when a has passed Z and /3 is descending from F towards 

VOL. XXIV. PART I. S 




64 MR EDWARD SANG ON THE MOTION OF A HEAVY BODY 

N, the point 7 must be approaching to Z, and it must reach Z just when a and (3 
have met at N. Thus the time in which 7 describes the arc MZ is just equal to 
that in which it passes from N to M. By the time that a has reached Z again, /3 
has reached L the extreme point of its motion on the other side, and therefore 
7 is at P the middle of ZL; lastly, when a has once more descended along 
ZPLN to N, (3 has descended along LN to the same point, and so 7 also has 
come to N. 

It thus appears that while the point a makes two complete revolutions, the 
point 7 makes only one. In the progress of this revolution the velocity of 7 
varies ; when at N it is half the sum of the initial velocities V A and V B , and 
when at Z it is reduced to be their difference ; so that the motion of 7 has the 
general characteristic of one due to the action of gravity upon a heavy body. 

13. If the motion of 7 can be truly represented by the action of gravitation 
upon a heavy body, we may determine the point from which 7 may be supposed 
to have descended, and the intensity of the gravitation which must act upon it, 
by comparing the velocities at the lowest and highest points of its path. Let C 
be the point from which 7 must have descended in order to acquire at N the 
velocity \ (V A + V B ), or at Z the velocity \ (V A — V B ), and put G y for the intensity 
of the gravitation to which it is subjected ; then 

V(G r . NZ . CN) = * (V A + V B ) ; J(G y . NZ . CZ) = J (V A - V B ) . 

Now according to Article 10, 

V A = NE . NZ ; V B = NE . NF 

while if we make ZI a mean proportional between CZ and ZN, and join NI, we 
have 

NZ . CN = NP, NZ . CZ = IZ 2 , 

so that • 

V(G 7 ) . NI = J NE (NZ + NF) ; J(G y ) . IZ = \ NE (NZ - NF) , 

whence NI : IZ : : NZ + NF : NZ — NF ; a proportion which enables us to deter- 
mine the position of the point I, and, consequently, that of C. 
Taking the square of each term of that proportion we have 

NP : IZ 2 : : NZ 2 + 2NZ . NF + NF 2 : NZ 2 - 2NZ . NF + NF 2 

whence 

NI 2 : NZ 2 : : (NZ + NF) 2 : 4NZ . NF 

and consequently 

_ NZ 2 (NZ + NF) 2 , _ NZ + NF _ NZ NE + NZ , 

i>J - ~ 4NZ . NF ».«*-■"* 2V(NZ . NF) 2V(NE . NZ) 



ALONG THE CIRCUMFERENCE OF A CIRCLE. 65 

whence also 

NC = (NZ ,ti^ F)2 ; 4NF . NC = (NZ + NF) 2 . 
4NF ' 

14. Having thus determined the position of the point C, we can determine 
also the intensity of the gravitation for, putting for NI the value just found, 

^• NZ 2 Xz-NF) ^ NE(NZ + Nr) 

whence G y = NZ . NE ; so that the intensity of the gravitation for 7 must be a 
mean proportional between those for a and ft. 

15. A descent from C under the influence of gravitation of the intensity 
NZ . ZE would cause a heavy body to have at Z and at N the very velocities 
which the moveable point 7 has at those places ; and we have now to inquire 
whether the same influence would give to that body, when at any intermediate 
point, the corresponding velocity. Before treating of this matter generally, it 
may be instructive to inquire into the velocity of the point 7 when it is at M the 
middle of FZ ; the moveable point 7 is at M when a is at Z and ft at F, now at 
that instant the velocity of ft is zero, while the velocity of a, proportional to the 
square root of NZ . ZA, is represented by NZ . ZE, so that the velocity of 7 must 
thenbeiNZ.ZE. 

But the velocity of the heavy body when at M is given by the general formula, 

J(G y . NZ . QO) = V{G r . NZ (NC - NQ)f . 

Substituting for Gy the value above found we have 

vj = NZ . NE (NP - NM 2 ) 

but since M is the middle of the arc FZ 

2NZ : NZ + NF or 2NE : NE + NZ : : NZ 2 : NM 2 



wherefore 



= NZ 2 NE + NZ ; but NI 2 = NZ 2 < NE + NZ > 2 
2NE 4NE.NZ 



wherefore 

NI 2 - NM 2 - NZ 2 pE 2 +2NE.NZ + NZ 2 _ 2NE.NZ + 2NZ 2 } 
I 4NE.NZ 4NE.NZ J 



NE 2 - NZ 2 ZE 2 

= NZ 2 ,~L ™„ = NZ 2 - 



4NE . NZ 4NE . NZ 

and consequently 

vj = \ . NZ 2 . ZE 

or 

v =iNZ . ZE 



66 MR EDWARD SANG ON THE MOTION OE A HEAVY BODY 

and thus the velocity at M due to a descent from the level of C is exactly that 
which the moveable point 7 has at the same place. 

16. We may now examine the velocity which this same heavy body would 
have at any intermediate point as 7. The general expression for that velocity is 

v y = J {G y (NP — N7 2 )} = J {NZ . NE (NP — N7 2 )} 

but since 7 is the middle of the arc a (3, 

N7 2 = } {NZ 2 + Na . N/3 - Za . Z/3} 

subtracting this from the value of NI 2 and simplifying 

NE 2 . NZ 2 + NZ 2 . NZ 2 + 2NE . NZ . Za . Z/3 - 2NE . NZ . Na . N/3 



Ni 2 - N7 2 = 



4NE . NZ 



Now NE . Na = NZ . N/5 so that the continued product NE . NZ . Na . N/3 may be 
written either NE 2 . Na 2 or NZ 2 . N/3 2 ; writing it once each way we obtain 

N1 2 _ N 2 „ NE 2 . Za 2 + 2NE . NZ . Za . Z/3 + NZ 2 . Z/3 2 
7 ~ 4NE.NZ 



_ (NE . Za + NZ . Z/3) 2 
4NE . NZ 
wherefore 

, 7=7 {NE. KZ (NE.Za E+ KZ. Z ^ | =HNEZa + Nzzft; 

but we have seen that NE . Za is the velocity of (3 at the point /3, NZ . Z/3 that of 
a at the point a, so that 

and thus, at every point of the circumference, the velocity of a body projected from 
N with a velocity due to a descent from Z, and acted on by a gravitation having 
its intensity represented by NZ . NE, is equal to the velocity of the middle of the 
arc a /3. 

17. The motion of the body 7 round the circumference has for its conjugate 
that of a fourth, which we may name 8 ascending from N to K, and thence 
returning to N, while 7 rises from N to Z, and proceeding onwards, returns to N ; 
the conjugation being analogous to that which connects the motions of a and (3. 

Hence, if we inflect the chord N£, a fourth proportional to NZ, NK, and N7, 
we shall obtain the point at which the body 8 is found when 7 is at 7 ; and if 
we make G§ a fourth proportional to NZ, NC, and G 7 , we shall obtain for the in- 
tensity of the gravitation to which 8 must be subjected 

NZ : NC : : NZ . NE : NC . NE = G.. 



ALONG THE CIRCUMFERENCE OF A CIRCLE. 67 

18. In this way we have obtained two pair of conjugate motions, the periodic 
time of the second pair being double of that of the first, and the intensities of 
gravitation being 

G = NZ . NZ 

a 

G^ = NZ . NA 

G = NZ . NE 
y 

G s = NC . NE 

such that any one of the four motions being known the other three may be found. 

19. Here it is to be observed, that the periodic time of 7 and 8 is double that 
of a and /3 ; in order to bring it to be the same, we must quadruple the intensities 
of the gravitation acting on these bodies, so that for all the 

Periodic Times alike 
G a = NZ . NZ , G^ = NZ . NA 

G = 4NZ . NE , G. = 4NC . NE . 

20. And if the intensities of gravitation be supposed the same for all the four 
bodies, their periodic times will then be proportional to the square roots of the 
preceding intensities : so that if we put T a , T^, T , T s for the periodic times on 
the supposition of one gravitation, we have 







Gravitations 


alike 




T 

a 

T 

y 


= NZ ; 
= 2 V(NZ 


• NE) ; 


T = 
T = 


NE 
■2V 



21. These two pairs of conjugate motions are so connected, that from one of 
them the other can be found, the law of connection being contained in the pro- 
portion 

NI: IZ: : NE + NZ : : NE-NZ 
or in 

NI + IZ: NI-IZ: : NE : KZ . 

If then from the pair a, (3, we deduce the pair 7, 8 ; we may again from this latter 
deduce another pair of conjugate motions which we may mark 7^ 8 l ; and from 
this again another pair 7 2 , 8 2 , and so on without end. Or if we regard 7, 8, as the 
original pair, and deduce a, /3, from it, we may thence deduce a new pair a x , /3 V 
and from that again, another a 2 , /3 2 ; and so on, so that we have a progression of 
conjugate motions extending indefinitely each way, and such that any one of the 
series being known, all the others can be thence deduced. The latter branch of 
the progression, viz., that from 7, 8, to a, /?, and thence onwards is that which 
is available in our research. 

VOL. XXIV. PART I. T 



68 MR EDWARD SANG ON THE MOTION OF A HEAVY BODY 

22. The periodic time of a body descending from C is deducible from that of 
one which has the velocity belonging to a descent from A ; that again is deducible 
from the motion of a body supposed to have fallen from A v and so on. Now, the 
distances NA, NA 1? NA 2 , &c, increase with greater and greater rapidity as we 
proceed, so that after a few terms NA may become enormously great as compared 
with NZ. But EZ is proportional to the velocity at Z, while NE is proportional 
to that at N ; and the ratio of NE to EZ must approach nearer and nearer to a 
ratio of equality as the point A rises ; so that when NA is very great, the velocity 
becomes almost uniform, and the periodic time of the motion becomes the 
quotient of the circumference by that velocity. In this way, the study of the 
law of this progression may conduct us to a knowledge of the periodic time of the 
motion of 7. 

23. Analogously the distance NB is deduced from NC, from NB again we may 
deduce NB 1S thence NB 2 , and so on; and in this manner, we may reduce the 
question of the time of descent in the arc KN, to that of the time of ascent in 
an excessively minute arc. 

24. Attending first to the case of oscillatory motion, let it be proposed to 
compute the periodic time of a body having its velocity due to a descent from 
the level of D. 

For this purpose, let us put B for the angle NZK measured by half of the 

extreme arc NK, and B a for the angle NZF measured by half of the arc NF ; 

then 

NK = NZ . sin B , KZ = NZ . cos B ; 

but 

NZ + ZK : NZ - ZK : : NZ : NF , 
wherefore 

1 + cos B : 1 — cos B : : (cos £ B ) 2 : (sin $ B ) 2 : : 1 : sin Bj 
and 

sin B 1 = (tan J B ) 2 . 

But it has been shown in article 20 that the times of descent from K and 
from F, there marked by the symbols T s and T^ are in the ratio 2\/(NC . NE) : NE 
or of 2\/NC : a/NE. It is now convenient to indicate these times by the charac- 
ters T sin. B and time B x , so that the above proportion may be written 

\/NC : a/NE 
2NI : NI + IZ 

2NZ : NZ + ZK 
2 : 1 + cos B 

1 : (cos£B ) 2 

(sec J B ) 2 : 1 

so that the time of descent from K is 

time B = time B 1 . (sec ^ B ) 2 . 



time B : time B 2 



ALONG THE CIRCUMFERENCE OF A CIRCLE. 



69 



Hence the following very simple construction : — Having made NS the fourth 
part of the arc NK and drawn a horizontal line through N, join OS and produce 
it to meet the horizontal tangent at T ; draw TU 
perpendicular to OT, meeting ON produced in U ; 
lastly inflect NF double of NU ; then the time of 
descent along KN is to that of descent from F to N 
in the ratio of OU to ON. 

By repeating this operation in regard to the arc 
NF, we should obtain a much smaller arc, and 
thence again one still smaller, and so on ; the 
periodic times in these successive arcs bearing 
known ratios to each other. Now it is obvious, 
from a glance at the figure, that these arcs, which 
we may denote by 2B , 2B 1? 2B 2 , &c, form a very 
rapidly decreasing progression ; and that the ratios 
of which ON : OU is the first, approach at the same 
time to a ratio of equality ; hence the time of descent along KN may be deduced 
from the time of oscillation in an exceedingly minute arc. A very familiar in- 
vestigation shows that the time of oscillation in a small arc is almost independent 
of the extent of the arc ; but instead of founding on this well-known proposition, 
I prefer to deduce the truth of it from our present considerations. 

25. If we suppose the arc NF of figure 2 to be very minute, the height NA, 
which is inversely proportional to NZ, must become very great in proportion to 
the diameter NZ, and hence the velocity at the point Z must be nearly equal to 
that at N, the two being in the ratio of ZE to EN ; and the time in which a body 
descending from A describes the circumference must always be greater than that 
in which another moving with a uniform velocity equal to that at N would de- 
scribe the same circumference. Putting g for the actual intensity of gravitation, 
the velocity acquired by falling from A to N is 

V A = */(2g . AN) 




so that, as ttNZ is the length of the circumference, the value of T A must be 

NZ 



greater than 



ttNZ _ //NZ\ /NZ //NZ\ 

<s/2<7 . AN - W V ty ) ' sl AN ~ ^ si \~2g~ ) ' 



NZ\ NF 
NZ 



while, since the velocity at Z is to that at N as ZE to NE, the same time must 
be less than 



//NZ\ NF .,_, 

V {~w) m ■ sec Nzr - 



26. Now we have seen that 

T a : Tp : : NF : NZ 



70 MR EDWARD SANG ON THE MOTION OF A HEAVY BODY 

wherefore the time of descending from F to N, and thence rising to L on the 
other side, is between the limits 



-v'(f)«W(f) •-"«*. 



which limits approach closer to each other when the arc NF is made smaller. 

27. Resuming now the investigation as in article 24, we find that the time of 
oscillation from K is 



time B ^(sec §B ) 2 tt J ( ^- j 

^r(sec I B ) 2 nj (^ ) . sec B v 



Continuing the same progression another step by making 

sin B 2 = (tan | Bj) 2 



we find 

time B ^ (sec i B ) 2 (sec } B,) 2 w J (^\ 

^: (sec * B ) 2 (sec h BJ 2 tt J (^j . sec B 2 ; 

these limits being now closer to each other, since B 2 is a smaller angle than B r 
If, then, we continue the progression indefinitely, by making 

sin B 3 == (tan J B 2 ) 2 ; sin B 4 = (tan J B 3 ) 2 ; &c. 
we shall obtain for the entire time of an oscillation in the arc 4B , 

time B = ttJ fi^\ . (sec § B ) 2 . (sec J B a ) 2 . (sec | B 2 ) 2 . &c. 

28. As an example of the calculation we may require the time of oscillation 
over an arc of ] 80°, which is the extreme limit of a pendulum with a flexible 
thread. In this case B = 45°, whence log tan \ B = log tan 22° 30' = 9617 2243 ; 
wherefore log sin B 1 — 9*234 4486; B 1 = 9° 52' 45"42 ; from this again we have 
log tan 1 B 1 = log tan 4° 56' 22 "-71 = 8-936 6506; log sin B 2 = 7873 3012, giving 
B 2 = 0° 25' 40"-74. And once again, log tan iB 2 = log tan 0° 12' 50"-37 = 
7-572 2861; log sin B 3 = 5-144 5722, B 3 = 0° 0' 02"-88. Here we observe that 
the log-secant of B 3 does not differ from zero by unit in the seventh decimal 
place ; and that, therefore, we have brought our limits so close together that the 
difference cannot be appreciated by help of the ordinary logarithmic tables. The 



ALONG THE CIRCUMFERENCE OF A CIRCLE. 



71 



logarithm of the ratio of the time of oscillation in a semicircumference to that in 
a small arc is thus 

Log sec \ B = 0-034 3847 
Log sec iB x = 1 6160 



Log sec \ B 2 



30 



0036 0037 x 2 



1180311 



0-072 0074 



In other words, the time of oscillation in a semi-circumference is to that for a 
minute arc as 72 to 61 very nearly. 

When the arc is nearly a whole circumference, the steps of the progression are 
more numerous, and the computation may, with advantage, be systematically 
arranged. I subjoin the work for an arc of 320°, with logarithms to ten places. 



n 


JB„ 


2 log sec ^ B„ 


2 log tan £ B n 


B n+1 





4°0 00 00000 


•23149 20670 


9-84762 70684 


44 45 21-339 


1 


22 22 40-669 


6800 53042 


922920 47378 


9 45 34-359 


2 


4 52 47180 


315 40158 


7-86265 75152 


25 03-441 


3 


12 31-721 


57684 


5-16071 41918 


2-986 


4 


1 493 





=log 200750740 




•30265 71554 = 



Thus, even in this extreme case, four terms of the progression are sufficient. 

These examples show that for all cases in ordinary clock-work, or in experi- 
ments on the length of the pendulum, the time of oscillation is sufficiently well 
represented by the formula 



timeB = 7r N /(i).(seciB) 2 



B being one- fourth part of the entire arc of oscillation. Hence the number of 
beats per day is proportional to the square of the cosine of the eighth part of the 
arc, and the daily retardation to the square of the sine of the same eighth part. 

29. From the periodic time of an oscillation that of the conjugate continuous 
motion may be readily deduced ; and thus, so far as the entire motions are con- 
cerned, the theory may be said to be complete. The investigation of the time at 
which the moving body arrives at any proposed point in its path is carried on by 
the application of the principle just explained ; but as it is of comparatively little 
interest, and, at the same time, more tedious, I shall not, for the present, go into 
its details. 

VOL. XXIV. PART I. U 



a» gi, Hi m :bL (» »» II! 


•f.. 1 i i_i_ ik. i ip .-, . X" •! 'in 


-+- ' - " y 


t mx 


1 , . ± . h i- M-4-J «v- 






^^ 


: .. ± ± . r n T ! i- a^ ! 


i . 1 1 1 1 1 ■ ! 


: 1 -1 1 ' ! "» . . HW-- 





■ ■ ■ T T T 






III 1 1 J 












I rTTII 1 


cisi'i:. Blnci Iron Bar -Nakec. 


tjsEl, Subsidiary B aijran JT? 1 


[ 1 


. x i a i- ■ 


., Otamsft./,.,- k*rii A J«.«.- Hmtannrtal 


' ' L ' ' 


,„, 44tx~ i r , [[-W-1 n mT'P « + 


\ 1 ! . ElfalJtd Scale of Lonftl} 


,1/W, «. , 1 wl,rp,.li, r d. 1 l^_ » 






' ■ 




v XX 


k B„».,i j,^, ,„}„^i :■«», a. __ ._ "j 






| -4---H- 




v 




^ ' 


7?i/ shivtrg run? it tin /mt.-.t/ piirrofthepl.itesttmi h. 


v 4 1 ^ 








HI ' 1 


XI ° 


S ■ 


1 


/ 's ! 1 1 


" " V x 






1 1 ' 


i» " " 4 " X 


- ' X _L X _1_ 


H \> - X _ - 


.J ,.. ^| l . 


_J - A*. 


: :•_ _. 


~t--£--- x ;;: xxxxx: xxxxx^::::::: 


^ a ... 


™ " - i ^5 




"T" \ 4 _ I - 




■ 3 








t \- ' X 




m I 4 * 3 








~ - n V 5 




_V 4 




Z 4 y 








™. L c - l. : 




4 - 5 - 




r,L ^ X - ' " V - 


I 


XT l V _ 




«* _| 4 \ I < 








- ■ X 




3lV V X 




ii J 






ti -r 


V $ 3z . - 




- ,-4 ^ * 


.. . ■ Of KVJK OF B'l'ATJU'A'li ll'»;:v l t"K'|tA'i|' l P Mi 


■ S^ t- -t i 




. i _ 


cas:;3. SubsUiarr. Jii-iKi-nn S?,2 










6~, 1 ~ ■ " 




I ' 




-4 - .3-' X ■< 


1 


.0 ax * 




% \ 




* - V ti 


"XLi i, 


\ 3 






li 1 -■ — 


* \ \ i Tin 


1IL- IW in \Ifi III 1 . \llr 






- - jsS 3 X X_i " 


.-^ 4x 


- tzl aX \ 






«. 


1, ^ 




3f £a ^ 


X 


5 4 


ill 1 


■i -, ■■. ; 


. ........ 




„, 




... 1 




1 1 


- " i %•■ 


1 , — 


- - -+r- ' * - 


1 1 


» ■' .... i\ 1 ' _L •■■■' ^ 


III 


ji i 4 \ ' — r f 




: '4 1 N. i 




BflNhL 1 1 ' l 


X 


fti- M 1 1 l> M 




: ' ! T*lw ■ j-N. 




. 4 + r&l'-L. i n-J ! U : 1 II 




■flk '- 4-4- -&*t-'"-- : ."H i /■; 


1 1 1 • 


'">- 4-4 ' ■ A-nA ■ fc£ 


II 1 








111 






s t.4 ■ •:;.■- 1 v- — 


I-—- ■- 






„ __ < +*fff _ | , , .^tl-'TlUf-u^ .. ^X 


xxiTm.I";;;;;- 



i,;j.I.jL/.^uuw...J:d// 



.„„ Sl'sO* ft B* iO? SO' «» JO» I» 10» JO* SO- p, 


Tranj.Jkp Soc.Zdin n. IV. rd.mv. i>SL 








\ 


■ \ jl| 1 1 


V X 




v 




.X . . i 




\ 




\ 




\ ; 


pr^p rengje^mctnj*. of liarJnTunns «T tin' tiiui' 








i V C(A"se I. .14 Ini'h [rrni Bar ,\ nilii-.d 


\ X 4 l 




\ ^X rjsfl Rnlisidiar v Til ;i ., i-ajnW™ 1 








X ^xt ' 








X X _i ' 




\ s, 




V !» , 




._ - X. \X 


i i , "wsAjjw as ' r '* J ! X " ^ 




' \ 






J d S N 5 !, 




jLX SV 




- 


l 3 : ~~ «x 


4X5;% vfx 


»» 7- -» "+- 




■ " - x 


■ ^^^i 


U i Jj 


A a^^ rvb 




* ■-Nq ^^- - 




"*X X=_ 




»5.-h-N^- - ..-i_ - - 








4X 


\ - 




C " ' X " " 




-^TT A, 


, \ 






_ . . . 


X 


C : -X - 




i=o \ . L -. «> 


X 


15 


T i: x x. 






r t 


Time Scale HaroTh i2) 


5 




no . . J 




x v x 


T i in ii S - ii i f Ma r o'li !« 


^ SHi»"> 




' X 


1 , . . ■ 1 . . . 1 . . ■ . ! l 


\ 


! ■ i 'si 1 


TV- a 


*■ a> X •■:,*' [ 1 *t 


i • \ \ 




^ V- ' V 




5 S 




^ \ t 




" - ^ ^ a 








3 X X 




X - Vj t $ 




t v| ^ 


' X ' imsi T ■SiLlisiflin.ry Biiifli-ajii V2 




\ " 




^ 1 , ' 


_.. V 5 


s, ..„„, ■.„■„ .1 Tim.. S.i, 1... 


5'2 X 




- - - - - LS X \ 


s r 




in 


- - - ■ ■ xx i 




XT _ \2K _ X 


N v r 


--- -- X — - X X 




'■ 3 




\1& XX 




- -1- - _ - X§ \ 


X " 


\3" n; 




— .- *,-*». " ^ 




. X. X. s 




h vi- X X " L 




S S X 




- - <s X 


**— ^1 


r > X 




+- - .. x^*- : X 




»■ ; % *?»■ . \ — t- [»,„» 




V T* -v \ i V. 












\ rj.s:; I. Vl.inli.ir. Ul.itir.iin Nl'.l <& 




~ X 




.!• 1 <n li.Mli-l.irUi.T mlninna ' v » 


■ 










■ x ■> . 


-++- 






'X, - X 








' 






„. 


* 301? H K ^,1. 


" 



V 



*A, 



i s, : •* : u -=j k 


^ -| |M j ■ - • - y, § - i s ? « s I | I I ^ 










r- 


QJ f J 


i> % i . — U U 


— if 1 PX — -5 s ! ?'■■ 




t " r " :: s ' ' r ; " 








1 1 


r ° u 






\ w r 








zzziz] zzzzzz*: a j z |± 


'. £ < c _ - 


= : ^ g 


SZE , 




tM 






U'Sr 5> •- "== ij c S S 4-rf c -Sz 




44fci - - ^ , H •. -^ ft 1 TST 6 








HeR! ? . § - ~ — ~ — - « . _._ n 




■b i, h - >■ 




1 i"X £ -' 1 * ; . S - « ■ 


1 .... ' B i M ^ 3 1 


■OS ff r s s ' - ► 




"TTO ," MM " S 




f • g, ■ 1 : :|t E X * u 




Hri ff i i r- 


\ -( >(i I Z< i . 


Re: 1 m S £ 3 *"& " h 1 - \ u 


» N - 3 ■ 1: o & '- 'i a 


■BlJ-y m U - -|"- :zzzzz-zxzzzxxzzzzzzzzzzzzzzzl 




SJiS 8 it ■ r > i \ - _ - x 




in? s ! i s \ f- s 


- A- - r ■* " h h 2. - 


pk, s v ■ - '?, > - ' * 


s - a ■*£<]§ ^ 


■fmr • t ran rah " " _T T -4 eh* X 




tE !n >' ^ \ t 


X 6 j g r »i • ... 


tP K a « " \ 


\ < c ■» s u 




\ 2 m-k p — - -- -1 


« ci 1 zt: z ~~ " i V ' ' " " 


a * | M 8 m 1 r. 2 j 


Hi - e V P f A *- ^' 




4c . ~ ■ i - ' c 






\ i it j a'3 t x 


5j !| «" '3i V 


x t; xa * •, 




B ■ fl ! ffl : ■ •» / h s 


# g - - E -$".g^ ^ ■ -- - i o - ■ S 


v ; tes a « / " 




\ o 1 / 


----© fe iJ 1 t ■ X M 








.-§£.[£. fC,;5 .$ , . \ i " > ' 


a \ 8 w / g 


. £t|i g | • 1 1- \ a \ 


\ 1 I 


m % £ 




|5f J | A T 


\ ' J 






11 . i.tt . Z a. o \ ' 


e T " \ 9 f » 


IP I s -i- * v * v -i-i- 




._ - 5 " Z X " "" ■ • 5 zh " 




_ \ N s hx 




V v \ i 


^S' \ \ 


■ : ^ <r ^ n V 




= ■ A | | ■ v " - " s ^= X Th 


-<L rl\o / « 






H * 




v- - zh V a X I v 




■ i , x . ..j „ H ^jzz*^ " i 4 " 


m - \ , J i J a 


zhh v » X s i i i\i 


8 \ » .. . T' 


iJ — J» J_ 4- ^ - ■ \ d N i\ 


t \ 


: < . zhzX 


1 \ / 


.Zl i ^ vi __ r . a. . Z^ 


iZT" "• to \ ' : • 


IL . _ ■ L N, s As. fc l^sl a. X ^ 


\ ■ o If- - , • / o 


"X ! K d \ " i i 


x . | "i : - - ...../ . T 


B4-- I i . * - ■ X xzzk 




el L X_ ^ X 4X ■ -LAiX- ^a@Z[ " X ZK 


N I \ 


ztt-^±- \ Etf" -Hzk- 


Eg=d W+ \ ' " " " " '■ ' ' } ' ' v j 




l % % t s s ' s§ssfig||i|g 



( 73 ) 



VIII. — Experimental Inquiry into the Laws of the Conduction of Heat in Bars. 
Part II. On the Conductivity of Wrought Iron, deduced from the Experiments 
of 1851. By James D. Forbes, D.C.L., LL.D., F.R.S., V.P.R.S. Ed., Principal 
of St Salvator and St Leonard's College, St Andrews, and Corresp. Member 
of the Institute of France. (Plates I., II., III., IV., and V.) 

(Read 20th February 1865.) 



CONTENTS. 



Introduction, 



§ I. Statical Experiments — Graphical Interpola 
tions — Equations to Statical Curves, 

§ II. Experiments on Cooling — Graphical Inter 
polations — Equations, . 

§ III* On the Proportion of Heat dissipated by- 
Radiation and by Convection, 

§ IV. The " Statical Curve of Cooling"— Reca- 



Page 

73 



75 



87 



95 



pitulation and Application of the Method 
of deducing the Conductivity, 

§ V. The Method of this Paper applied, under 
the usual assumptions of the Theory of 
Conduction, as a first approximation to 
the determination of Conductivity, 

§ VI. Final determination of the Conductivity 
of Iron at various Temperatures, . 

§ VII* Concluding Remarks and Suggestions, 



Page 



97 



99 

101 
106 



INTEODUCTIOK 



The Articles are numbered in continuation of those in the First Part of this Paper. 

39. In the first part of this paper, read to the Royal Society of Edinburgh in 
April 1862, and published in their Transactions,! I explained the principles of a 
method devised by me in 1850 for ascertaining the absolute conducting power of 
substances capable of being formed into long bars ; and I also stated the general 
results of experiments made in 1851 on the Conductivity for heat of wrought 
Iron. 

40. I explained in Art. 14 of that paper, that the publication of the results 
had been for ten years withheld, partly in consequence of the state of my health 
which completely interrupted the experiments, but still more from the defective 
graduation of some of the thermometers used, which made it necessary to submit 
the instruments to a careful scrutiny, and to repeat with the duly corrected 
numbers the whole of the elaborate projections of the curves and calculations 
from them, on which the accuracy of the final results of course depends. 

41. I stated that the friendly aid and exemplary patience of the late Mr 
Welsh of the Kew Observatory had supplied me with data for correcting the 
readings of the most important, and at the same time the most inaccurately 
graduated of the series of French thermometers employed in these experiments. 

* Sections III. and VII. have been added to this paper since it was read. 
f Vol. XXIII. p. 133. 

VOL. XXIV. PART I. X 



74 PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 

Without his help the present corrected reduction of the observations could never 
have been made ; and even with the aid of the tables kindly prepared by him, it 
has been a work of no small labour and anxiety to bring to one strictly accordant 
scale the whole of the observations made with eight or ten thermometers, none 
of them deserving of being called standards, and in most of which the zero 
appears to have oscillated at different periods. 

42. I have thought it unnecessary, as it would certainly have been most 
tedious, to print in this paper the crude observations and the numerous tables of 
reduction formed for the scales of the several thermometers. I have thought it 
sufficient to give the corrected results, which, in many cases, are the mean of 
independent readings of different thermometers. 

43. Besides the correction of scale errors, an important correction required 
to be applied in order to reduce the readings to what they would have been had 
the column of the mercury in the thermometer partaken of the temperature of the 
bulb. Owing to the small transverse dimensions of the bars, whose temperatures 
were to be ascertained, the bulb of the thermometers was often little more than 
covered by the mercury with which the holes in the bars were filled (Art. 20). The 
stems were therefore necessarily exposed in their whole length to the temperature 
of the surrounding air. In the case of the higher temperatures to be measured, this 
correction was not only large (amounting sometimes to 3° Cent., always additive), 
but also in some degree uncertain, owing to the ascending currents of warm air in 
the neighbourhood of the heated bar, and enveloping the stem of the thermometer.* 
However, I believe that the formula in the note below leads to pretty accurate 
results, checked, as it has been, by occasional observations of a small auxiliary 
thermometer suspended in the air, touching the stem of the thermometer to be 
reduced, about its middle. 

44. The hotter thermometers are probably slightly over corrected. I have 
stated that in extreme cases this correction amounts to about 3° Cent., a quantity 
which may possibly be erroneous in some cases to one-tenth of its amount, but 

* The form of the correction is very simple, being 

Degrees exposed x Excess of Temp, shewn over air. 



Dilatation of Merc, in Glass for 1° Cent. 

always additive. If T he the temperature as read, t the temperature of the air, and a the scale 
reading of the commencement of the stem of the particular thermometer, the correction is very nearly 

+ (T-a) (T-t) 



6400 

Since t and a are usually small numbers, the correction increases nearly as the square of the tem- 
perature to be measured. 

Fortunately, the precision of this correction is not very important to the result. It chiefly 
affects the actual temperatures ; for it will be more fully seen hereafter, that if the same instru- 
ment be used in the dynamical and statical experiments, being exposed in precisely the same way, 
the measures will be relatively correct, and the deduction of the conductivity will not thereby be 
sensibly affected. 



THE LAWS OF CONDUCTION OF HEAT IN BARS. 75 

I hope rarely so. Much larger corrections would have been inevitable at the 
highest temperatures (about 200° Cent.), had I not invariably employed for these a 
thermometer in which about 110° of the mercury was expelled from the bulb into 
the cavity at the top of the stem. The corrections for the reading of this thermo- 
meter were determined by Mr Welsh with extraordinary care. As its indications 
only commenced about the boiling-point of water, the length of the column 
exposed to the air was comparatively short. 

45. For the principles on which the experimental investigations are founded, 
I refer to Art. 5, &c, of the former part of this paper. It will be recollected that 
there are two distinct classes of experiments, in one of which (the statical) the 
permanent temperatures at different points of a bar are to be observed ; in the other 
(the dynamical) the velocity of cooling of a short bar of similar section, uniformly 
heated at first, is to be ascertained. I shall now proceed to describe these experi- 
ments severally more in detail than I have yet done, and to classify and discuss 
the results. 

§ I. Statical Experiments. 

46. The Apparatus.— A general account of this has been given in Arts. 
1.7-20. It will, however, be rendered more intelligible by a reference to Plate I., 
fig. 1. The long wrought-iron bar AB was supported on a wooden frame CD 
by means of one fixed support E, and two moveable props F, Gr, which were all 
of wood, and were brought to a blunt edge at top, on which the bar rested, at 
about 15 inches above the top of a massive table, which stood in a spacious 
apartment attached to the Natural Philosophy Class-room (Edinburgh Uni- 
versity). No fire was allowed during the experiments, and the south shutters 
being closed, the room was lighted from the north. At the end of the 
bar, towards the left side of the figure, was attached the heating apparatus, 
a cast-iron crucible H, usually filled with just-melting lead. It was kept 
hot by means of the powerful gas-furnace I, with a double metal chimney 
and two concentric rows of burners. The gas was derived from the main pipe 
by a flexible tube L, and passed through one of Milne's patent gas regulators, K, 
with a view to obtaining a uniform flame, which, however, remained subject to 
occasional fluctuation. The connection of the crucible with the conduction bar 
will be best understood from the sectional diagram in Plate II. fig. 1. An 
internal flange a, a' was cast on the crucible, leaving a square cavity 2-5 inches long, 
into which the extremity A of the conduction bar was thrust, and was retained 
there by friction only. The exterior face of the crucible b c is almost vertical, 
and determines the position from which the distances of the thermometers along 
the bar are reckoned. Supposing the crucible itself to be maintained at the constant 
temperature of melting lead, it seems reasonable to assume that the bar A, so far as 
encased within it — that is, up to the zero line b c — may be regarded as having nearly 



76 PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 

the same temperature.* The gas flame and the violently heated currents of air 
thence arising were prevented from playing against any part of the bar by a piece 
of metal plate fastened by wire to the crucible against the face a b (but to prevent 
confusion not shown in the figure), while the whole conduction bar was farther 
protected from heated currents, and from radiation from the crucible and gas 
chimney, by three polished metal screens d, e,f, placed parallel to one another, two 
to the left and one to the right of the wooden support E. The square apertures in 
the screens were 0-25 inch wider than the dimensions of the bar, and they were 
supported in such a manner as not usually to touch it in any part. These screens 
very effectually defend the thermometers, as well as the bar, from extraneous heat. 
The first thermometer only — that at 3 inches distance from the zero line b c — is 
seen at g in the section, fig. 1. 

47. The conduction-bars have already been described in Arts. 17, 18. The 
more perfect one was 1-25 inch square, and fully 8 feet long, reckoning from the 
zero line above mentioned. It was used in two states, first, with a naked polished 
surface, and, secondly, when coated with thin paper. The other bar, also of 
wrought-iron, was 1 inch in the side and 7 feet long. In the present paper I shall 
discuss separately the results obtained with these two bars, presenting three quite 
independent cases, but which, as they ought to lead to an identical value of the 
conductivity of iron (assuming the quality of the bars to be alike), put the method 
here proved to a severe trial. 

48. Throughout the remainder of this paper, when I speak of Case I., I mean 
the 1^-inch bar with moderately polished surface ; Case II. is the same bar with 
paper surface ; Case III. is the 1-inch bar with naked, but less brightly polished 
surface. 

49. The thermometers were inserted in holes in the bar 028 inch diameter 
and about £ inch deep. They were surrounded by mercury or (in the hotter holes) 
by fusible metal. (See Art. 20, and also Plate II. fig. 1.) Nine or ten thermo- 
meters were usually employed, and in the case of the principal bar (Cases I. and II.) 
they were usually (though not always) spaced as follows, reckoning from the 
zero line a b on the face of the crucible : — 

0-25, 0-5, 0-75, 1, 1-5, 2 or 2-5, 4, 6, 8 feet. 

50. The method of using a single standard thermometer for obtaining final re- 
sults by the method of stepping, with its advantages, have been fully explained 
at Art. 22. 

51. " The free temperature, or that to be deducted from the readings of the 
thermometers, in order to get the true excess of statical temperature along the bar, 
was obtained by inserting a well-compared thermometer into a hole containing 
mercury, drilled in a similar but short bar of iron, supported in the free air of the 

* See, however, note to Art. 70, below. 



THE LAWS OF CONDUCTION OF HEAT IN BARS. 77 

room in the neighbourhood of the long bar, and similarly exposed, but without 
artificial heat." (Art. 23.) The arrangement is shown in Plate I. fig. 2. 

52. The gas furnace was usually lighted about 8 a.m., when the lead in the crucible 
was gradually melted. The readings of the thermometers were not recorded until 
about four hours had elapsed, and the experiment seldom lasted altogether less 
than eight hours, generally ten or eleven hours. It was difficult to keep the flame 
of the gas furnace steady, the " regulator" used for the purpose being apparently 
of little use. The lead in the crucible, after being quite fluid, sometimes solidified 
a little over the interior flange which grasps the bar. I at length found the best 
way of regulating the temperature to be, to keep the eye very constantly on the 
first thermometer in order, and whenever the slightest rise commenced, to dip a 
little cold lead into the crucible, and either let it melt or chill the mass by its 
contact, or the gas might be cautiously lowered. If the temperature was seen to 
be falling, the gas had to be raised. With experience I learned to keep the tem- 
perature of the three-inch hole within a range of 2° Cent, under favourable 
circumstances, the temperature being nearly 200° Cent. In some experiments in 
which solder was employed instead of lead, I used a thermometer whose bulb 
dipped into the crucible, where it stood about 460° Fahr.* My able assistant, 
Mr James Lindsay, learned to regulate this with great nicety. 

53. When the temperature had been for a long time quite steady at the three- 
inch (or hottest) hole, the thermometers, disposed, as has been explained, along the 
bar, were successively read, and the readings recorded. This was done from left 
to right along the bar with all deliberation, without regard to any possible change 
during the process in the temperature at the hot end of the bar, since any such 
change is comparatively slowly propagated along the bar. In like manner, in 
" stepping" with one thermometer from point to point of the bar (Art. 2), a 
slight change in the temperature of the source is immaterial, since the " stepping" 
is performed faster than the wave of heat can follow. 

54. A careful examination of the whole record of simultaneous readings was 
made, and those corresponding to the most stationary conditions of temperature 
were selected ; and these being corrected for scale errors and temperature of column 
(Arts. 42, 43) were entered, after the free temperature indicated by the little bar 
(Art. 51) had been deducted, in the following tables as the Corrected Excesses 
of Statical Temperatures in centigrade degrees. 

55. Looking cursorily over Table I., we may observe, Firsts that each day's 
observations are comparable only amongst one another, as no exact coinci- 
dence of the temperature of the crucible, or source of heat on different days, was 
attempted. Secondly, the bracketed observations are made with independent 
thermometers. Thirdly, comparing the first series for the bar covered with paper 

* By an oversight in the first part of this paper (Art. 19, note), it was stated that in this 
instance the thermometer was dipped in melted lead. 

VOL. XXIV. PART I. Y 



78 



PBTNCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 



a 




a 




< 




« 




o 




t— i 




& 




« 




a 




O 




(B 




a 




W 




« 




c$ 




a 




ft 
1 




1 

a 




a 




P5 




>— i 




o 




& 




a! 




O 


^ 


fe 


=o 


o 


w 




13 


•< 


O 


pel 


o 


O 


•< 


m 


■*^> 


03 


g 


a 


&- 


P 
O 


-8 






H 


•"^ 


< 


ss 


fc 


^8 


o 


a 




« 


O 


o 


,, 


<u 


a 




cs 


» 


P 


J. 


EH 


<u 


«j 


>Hg 


C3 

a 


O 


0-, 


■^ 






a 


<W 


H 






o 


a 


« 


< 






« 
S 

o 


*i! 


rO 


Eh 




CO 


3 






a 


<a 


o 


f= 


m 


M 


a 




t» 




m 




a 




o 




M 




W 




Q 




a 




&H 




o 




a 




c3 












o 




O 





.2 
© 






O 



p 

o 



© 



o 



p* 



*& 00 o >o O O 00 

CO CI NCOf p CM 

o© 6 6 6 6 6 6 



o 
6 



00 00 

1-1 1— I 
6 6 



CO 
00 



CO 



o o 



op 



6 



© C5 
6 CO 



00 00 
CI CI 



00 CO 



* >o 



CM CI 



Ol CI 



t-a 



a a 
SoQ 



* 

a co 
O oo 



CM ■* ■* 
-CM CI CM 



co 



00 



f oo 

OCi 

t-cb 



o 

CO 



CO 

6 



«5 »<5 

^H -+> CI 

O O OS 



-H <M 



O 
OS 



lO ID 



l>.p 
ib >o 
oo 



p. 2 

cs co 

pqw 

§^ 



00 

,p 








rf 


>~. 




M 


i-t 


1— 1 
1-1 


g fe 






& ,? 

^ 


<1 


Ph 


S-p 


1— 1 


<3 


C *3 


«s 




H* ^ 


oo 




r-1 




■73 


| 


Td 


M 




(H 


0* 


1— 1 


ed 


T3 


i— 1 


13 


S 


a 


g 








C£_ 


ou 



o 
6 



«5 >« 

i-H rH 

66 



o' 

1— I 

a 



o 
6 



o 
6 



oo 



o 
6 



OON00 
HihOO 



CI 

CI 

6 



cp o 



6 



6 



Oi p CO 
U5K5 13 



96 
co So 



.s 



O CM 

CO O 



o 



o 
6 



6 



CO 



p 



«1 

6 









Ci CO 



—I o 
I CO 






CO 



p 

1-5 



00 



13 

P 
C3 

CO 



.5 



CO 

1 

p- 

p 

si 



o 

1 — I 

o 
3 






is 



» .5 

c -^- 

.2nr 
"S S 

o o 
.2 S 
2.S 

s a 



o >> 



t- 


»a 


01 




-*-* 




o 


-S 


y 


*J 


a 


m 


i- 






9) 




^a 



OH 



THE LAWS OF CONDUCTION OF HEAT IN BAES. 79 

(April 15) with the last of the same bar naked (April 11), which were made in 
almost similar circumstances, we notice the prodigious effect of the increased 
radiation due to the paper casing. Though the heat at the origin may be con- 
sidered as the same, at a distance of only three inches the temperature in the 
second case was less by nearly 30° Cent. ; at thirty inches distance, the proper heat 
of the bar was but one-half of what it was in Case I. ; at four feet, one-third ; and, 
at eight feet, it had vanished in the second case, while it was still sensible in the 
first. Fourthly, it may be remarked that in Case I. the bar scarcely fulfilled, as 
to length, the implied condition of the experiment, which assumes that the 
extreme end of the bar shall be sensibly of the temperature of the air. As o- 3 
of heat remained at eight feet, and as the bar extended only a few inches beyond 
that point, it would appear that the conducted heat was not absolutely dissipated 
by radiation. The effect, which is to render the decrement of heat in the extreme 
holes rather too slow, is, however, barely appreciable in the deductions. 

56. Graphical Interpolation of the Statical Experiments. — As it was desirable to 
combine the results of the independent experiments in each of the three Cases, 
and to deduce the most probable temperature for any point of the bar, a graphical 
method was adopted as follows : — Large sheets of drawing-paper were provided 
covered with engraved squares one-tenth of an inch in the side. A horizontal 
line was taken to represent the distances reckoned along the bar on a scale of four 
inches to a foot, and at the proper intervals the observed temperatures (or rather 
excesses of temperature) were set off as vertical ordinates on a scale of 10° to 1 
inch. The general arrangement of the observations in this way is shown in Plate 
III. on a reduced scale for Case I. 

57. It is plain, however, that this primary projection could only apply to a single 
and comparable series of observations under each Case of Table I., since the tem- 
perature of the origin might vary from one experiment to another. One set under 
each Case was assumed as a standard series to which the others were to be referred. 
In Case I., April 11 ; in Case II., April 15 ; in Case III., January 11 (b). But as 
it is plain that for one and the same bar the curve of temperature has the same 
form, though it may deviate in position to the right or left along the bar, each of 
the other days' observations was separately projected on transparent cloth, and 
then laid on the engraved squares over the first projection. By moving the system 
of projected points to the right or left (taking care to keep the line of abscissae in 
each case accurately coincident), a position was easily found where the points to 
be interpolated accommodated themselves best to the general curvature of the 
fundamental series. 

58. This method of interpolating independent series belonging to different funda- 
mental temperatures has very great advantages. Had circumstances allowed me 
to continue these observations, I should have applied it more extensively. A 
clear instance of its utility will be seen by comparing the first and second row 



80 PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 

of figures in Case II. of Table I. The observations of April 16 were made with 
melted solder as a source of heat, which fuses at a much lower temperature than 
lead. The result is, that the temperatures in the 3, 6, 9 inch holes and those 
which follow, are intermediate between the temperatures shown in those holes in 
the other experiment. Thus, by varying the temperature of the source of heat, 
we may multiply indefinitely points in the curve without increasing the number 
of holes with which the bar is pierced, which is evidently undesirable. It would 
have been very serviceable for the interpolation of the numbers in Case I., had the 
temperature of the origin been expressly varied for this purpose. 

59. The general agreement of the independent interpolated observations has 
been highly satisfactory, as may be seen from Plate III., where the several sets of 
temperatures belonging to Case I. are distinguished by marks. 

60. A continuous curve was next to be drawn through the extremities of the 
ordinates, so as best to conciliate the whole of the observations. To draw this 
curve was a matter requiring great nicety and judgment, owing to the limited 
number of ordinates disposable. It is well known to every one who has used 
such projections, that to draw an interpolating curve advantageously requires 
that the rate of increment of the two variables shall not be excessively unequal. 
In curves like those of Plate III., which rise very rapidly at one end, and become 
almost or quite asymptotic at the other, it is indispensable to make subsidiary 
projections of different parts of the curve, in which the relative scale of the vertical 
and horizontal co-ordinates shall be altered. For the part of the curve between 
and 2 feet, the temperatures had to be contracted in scale and the abscissae 
expanded : while for the right-hand branch of the curve the contrary was done, 
even to the extent of magnifying the vertical scale of degrees tenfold, whilst the 
horizontal scale of feet was diminished fourfold, compared with the first pro- 
jection. For each of the three Cases (Art. 48), the statical curve was thus sub- 
divided and partially projected on four different scales, three of which are exhi- 
bited on the engraved Plate. The result of this close analysis and comparison 
has been highly favourable to the assurance of accuracy in the final results, since 
the interpolated temperatures for any abscissae are the result of two, if not 
three, projections of the observations on different relative scales. No numerical 
or other casual error could thus possibly escape detection. 

61. I believe that these curves, as now obtained with the ordinates immediately 
to be given, are favourable specimens of numerical accuracy and geometrical 
definition, considering the difficulties attending the experiments. Throughout a 
great part of the curves (and that by far the most important for the results), the 
temperature excesses of the bar, or vertical ordinates, may, I hope, be esteemed 
correct within a very small fraction of their amount. The following table (which 
may be regarded as summing up the whole Statical data) contains the ordinates 
of the curves corresponding to the three Cases of Art. 48. 



THE LAWS OF CONDUCTION OF HEAT IN BARS. 



81 



TABLE II. — Stationary Excesses of Temperature (prom all the Projections) 

adopted. 



Distance from Origin 
at Crucible. 


Excess of Temperature (Centigrade) of Bar above Air. 


Case I. 
1 1 inch Bar, naked. 


Case II. 
1J inch Bar, covered. 


Case III. 
1 inch Bar, naked. 


inch 
1 
2 
3 
4 
5 
6 

75 
9 
10-5 
I. foot inch 
3 
6 
9 
II. feet 
3 
6 

III. „ 

6 

IV. „ 
V. „ 

VI. „ 

VII. „ 

VIII. „ 


275-5 c. 
242-9 c. 
214-8 c. 
1905 
168-3* 
1506* 
134-7 
114-1* 
97-3 
84-0* 
72-0 
53-6 
40-8 
31-0 
24-2 
18-9* 
14-8 
9-33 
6- 15* 
4-0 
1-8 
0-9 
0-50 
0-28f 


260-5 c. 
221-7 c. 
189-5 c. 
162-9 
140-0* 
121-5 
105-9 
86-6 
71-3 
59-0 
49-2 
34-5 
24-6' 
17-7 
13-0 
9-45 
70 
3-8 
2-1* 
1-28 
0-47 
0-165+ 


282-2 c. 

243-2 c. 

2102 c. 

182-2 c. 

159 

137-5 :; - 

120-5* 
99-8 
82-8* 
68-6 

57-1 
40-9* 
29-5 
21-6 
15-65* 
11-5* 
8-55* 
4-95* 
2-78* 
1-56 
0-55 
0-13* 


The numbers marked c. are derived from calculation. See Art 68 below. 
The numbers marked thus * belong to points in the curve not closely ad- 
jacent to points of observation ; and, therefore, are less certain than the others. 
•f* 0*32 by mean of 7 observations. +. Mean of 4 observations. 



Adjacent to the principal curve of Plate III. is a dotted curve, which exhibits the 
remarkable change of character in the curve when the bar is coated with a highly 
radiating surface of paper (Case II., Art. 48). 

62. Formula? of Interpolation for the Statical Curves. — It was not originally 
my intention to have entered on the thorny enterprise of seeking equations 
to satisfy the statical curves of temperature. My original plan (Art. 6 of former 
paper) was to deal with Curves alone, or almost entirely. And when we do 
not wish to exceed the limits of direct observation, it is perhaps the safest, 
as well as by far the easiest plan. I wished, however, to throw all pos- 
sible light on the problem, for the benefit of those who may hereafter extend 
these observations. I also wished to obtain the greatest amount of informa- 
tion from the data at my disposal; and by means of formulae, to extend the 
results somewhat (though not far) beyond the limits of observation. It will 

VOL. XXIV. PART I. Z 



82 



PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 



be seen farther on (Art. 71) that a formula, however empirical, enables us to 
execute promptly and with confidence the otherwise tentative and uncertain 
process of drawing tangents to the curve in its higher part, in other words, of 

obtaining values of -j- upon which the final deductions mainly depend. (See 

Arts. 6 and 31.) 

63. It had been acutely perceived by Lambert nearly a century ago,* that 
the temperatures of a bar heated in the manner of our experiment would diminish 
in a regular geometrical progression. A more rigorous analysis led BiOTf and 
FourierJ to the same result, according to the physical assumptions with which 
they started. Biot and Despretz§ subjected various metallic bars to experi- 
ment, but they assumed the logarithmic law to be true, and endeavoured 
to accommodate their numerical results to it, as well as they might. Biot, 
in particular, applied to his (apparently excellent) observations, the method 
of least squares to enable him to draw a logarithmic curve through his points of 
observation, giving no attention to the fact, that the temperatures found did 
not conform themselves by any means to the a priori geometrical law, and that 
the laws of Probability could not be applied to them without ascribing extra- 
vagant and improbable errors to a large part of the curve of observation. || 

64. That the temperatures deviate systematically from the law of continued 
progression, will appear from the following table of the ratios of successive ordi- 
nates, taken three inches apart in the three Cases of Table II. 

Mean Ratio!! between Two Consecutive Ordinates 3 Inches apart, from the 

Numbers in Table II. 



Intervals. 


Case I. 


Case II. 


Case III. 


3 to 6 inches, 


•707 


•650 




6 to 9 


•722 


•673 


■687 


9 inches to I. foot, . 


•733 


•690 


■690 


I. foot to I. foot 6 inches, 


•753 


•707 


•719 


I. foot 6 inches to II. feet, 


•770 


•727 


•728 


II. to III. feet, . . . 


•787 


•735 


•750 


III. to IV. „ . . . . 


•809 


•762 


•755 


IV. to VI. „ . . . . 


•830 


•774 


•731 



* Pyrometrie. Berlin, 1779, p. 185. 

f Traite de Physique, vol. iv. p. 669. 

J Theorie Analytique de la Chaleur. 1822. 

§ Traite Elementaire de la Physique. 1836, p. 197. 

|| Compare Note to Art. 3 of this paper. 

*fT By " mean ratio," I intend to express, that where more than one 3-inch space is included 
in the Interval specified in the first column, the number which follows is the average decrement 
throughout that space. Thus, in Case I. the whole interval from II. to III. feet, shows a decrement 
from 24° - 2 to 9°33, which would result from the mean ratio of 0787, four times multiplied into 
itself. 



THE LAWS OF CONDUCTION OF HEAT IN BARS. 83 

65. It will be observed that in every instance, with the single exception of the 
final number of the Table under Case III., the decrement of temperature becomes 
materially slower as we recede from the heated end of the bar. The exception 
is of little weight, as it depends on the residual temperature of the one-inch bar, 
six feet from the crucible, at which point the warmth was barely perceptible. 
The statical temperatures of the bar therefore increase more rapidly than in a 
geometrical progression. I have found that there is a sufficient analogy between 
the curve of statical temperature which we are here investigating, and that of 
the tension of steam at different temperatures, to afford some assistance in the 
selection of empirical formula? in the present instance ; being in each case a 
modified geometrical progression, though here the progression of ordinates is 
more rapid than a simple continued proportion, while in the tension of steam 
it is less rapid. 

66. The most complete discussion of this class of formulae, and the methods 
calculating from them, is to be found in M. Regnault's Relation des Expe- 
riences sur la Vapear. The available formulae are reducible to three ; Young's,* 
Roche's, f and Biot's4 The two former contain three constants, the latter five. 
The last has been found the most satisfactory for the empirical representation 
of the elasticity of steam; and it is the only one of the three which can be 
regarded as applicable throughout the entire limits of experiment. The same is, 
I believe, true for the Conduction-curves with which we are now occupied. With 
five constants, five points of the curve may be accurately represented, and the 
intermediate deviations are of course inconsiderable. As none of the formulae 
(except the simple logarithmic which is found to be inapplicable) have any foun- 
dation in principle , the whole matter is purely one of convenience. For simplicity's 
sake, I used only the formulae of Young and Roche, but I now think that 
the greater labour involved in the application of Biot's formula would have been 
repaid by the directness and certainty of the results. M. Regnault has given 
rules to facilitate its numerical calculation. 

67. I have found the formula, — 

lo s"= A -rrW • • • • ■».(!■) 

(where v is the excess of temperature above the air at a point of the bar, whose 
abscissa, in feet, is a, and A, b, and c are constants), to represent tolerably well 
the temperature curve of Case I., as represented by the numbers in Table II. , 

* p — A (1 +at)'\ where p is the elasticity, and t the temperature, 
t log p = log a + ^-~ t . 
X log p = a + ba' + cj8'. 



84 



PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 



throughout the whole extent of the experimental curve.* But in order to follow 
the observations more closely, it seemed desirable to divide the curve into two 
parts, one between and 1*5 feet, and the other beyond 15 feet, and to employ dis- 
tinct constants for each. A like process was applied to the numbers of Table II., 
for Cases II. and III. In these, the variations of temperature along the bar being 
more rapid, the approximation of the formulae was less exact than in the first case, 
and a formula with three constants was insufficient to represent the curve through- 
out its whole extent. I found it advisable, in the case of the bar covered with 
paper (No. II.), to use modified formulae for the upper, middle, and lower part 
of the curve. I may add that it was found convenient to adapt the formula 
(Eq. (1.) of this article) to the calculation of the lower temperatures, by changing 
the origin to an arbitrary point some feet to the right, and by reckoning the 
abscissae in the opposite direction, thus rendering the second term of the equation 
positive instead of negative. To this end the equation was written, — 



log v = A + 



1+cc' 



when 



68. The coincidence of the various formulae with the experimental numbers of 



Table II. is shown in the foregoing Table. 



* The formula in this case would be, — 



log v— 272.7- 



•63374 x 
1 + -0956 a:' 



The following adaptation of Young's formula also represents the observations in Case I. very 
approximately. 

v= (-43027 + -09539 a)-"*"'. 











v by Formula 




x in feet. 


o by Experimental 
Curve. 


v by Formula 
(a -\- bxf. 


Difference. 


log v — 

, bx 
log a- — — 

\-\-cx 


Difference. 







o 


o 


o 










272-66 


. • • 


272-7 




0-25 


190-5 


190-5 


00 


1910 


+ 0-5 


0-5 


134-7 


135-5 


+ 0-8 


135-9 


+ 1-2 


0-75 


97-3 


9804 


+ 0-74 


98-23 


+ 0-93 


1-0 


72-0 


72-0 


o-o 


72-0 


0-0 


125 


53-6 


53-6 


00 


• •■ 


... 


1-5 


40 l 8 


40-41 


-0-39 


40-21 


-0-59 


2-0 


24-2 


23-75 


-0-45 


23-53 


-0-67 


2-5 


148 


14-52 


-0-28 






3-0 


9-33 


9-18 


-0-15 


9-08 


-0-25 


4-0 


4-0 


40 


0-0 


4-0 





50 


1-8 


1-91 


+ 0-11 


1-96 


+ 0-16 


60 


0-9 


1-00 


+ 0-10 


• •■ 


. . • 


80 


0-28 


0-31 


+ 0-03 


0-36 


+ 008 



THE LAWS OF CONDUCTION OF HEAT IN BARS. 



85 



















• 


TjH 


CI 


OS 


co 


CM 


rH 




CO 


tH 


CO 


CO 










qS <E 










CO 


.t- 


CO 


■* 


CO 


O 


CM 


o 


i-H 


O 


CM 


o 


© 


© 










P "> ' 










O 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


© 


© 


















1 


+ 


+ 


1 


1 


+ 


1 


+ 


+ 




1 


1 


1 


+ 




























, 1 




1 — , 




















O 
























rH 


CO 


M5 


CM 


CM 


CM 


05 
00 










'a 




















CO 


05 


CO 


t^ 


M5 


J^ 


M5 


M5 


rH 








■ 




















CO 


o 


05 


M5 


00 


■* 


rH 


© 


© 










O 




















M5 


tH 


CM 


rH 


















1— 1 


rH 




















1 ' 


1 — 1 


1 1 
































































fe 
















CO 


00 


OS 


.N. 


CM 




















o 


CM 


cm 


CM 


CM 


■* 


CM 


00 


CO 


r-l 


i-H 


CO 


Mi 






















a 


CM 


CO 


o 


CM 


00 


00 


o 


05 


CM 


N. 


o 


05 






















00 


tM 


I-l 


00 


M5 


CO 


CM 


05 


a; 


>o 


■* 


CM 






















o 

fa 


CM 


cm 


CM 


I-H 


7"H 


i-H 


l-H 
























































>C5 


M5 


lO 


CO 


MJ 


CO 








>>£ 










o 


MJ 


M5 


00 


oo 


rH 


05 


M5 


CO 


M5 


05 


M5 


M5 


i— 1 










Ja fc 










05 


J- 


o 


05 


CM 


*» 


o 


05 


M5 


00 


■* 


i-H 


© 


© 










» 9 










M5 


CO 


CM 


05 


co 


Mi 


tH 


CM 


rH 




















o 










rH 


rH 


r-i 
















































00 


CM 


CM 




^H 


CO 




C5 


rH 




CM 








*H . 








o 


CO 


■* 


© 


O 


o 


rH 


r-l 


O 


O 


O 


O 


O 


© 


© 




















































m 




SB g 








o 


O 


O 


O 


o 


o 


© 


o 


o 


o 


O 


O 


© 


© 


© 






a> 




5 ® 










+ 


+ 




1 


+ 


1 


1 


+ 


1 




+ 


+ 




+ 






P 
n 

en 














































H 
























■* 


tH 


o 


05 


05 


^» 


M5 
CO 






TJ 




a 






















HA 


CO 


05 


o 


CO 


CM 


rn 


I-H 






CO 
























-* 


** 


CM 


J^ 


CO 


rH 


© 


© 






-a 




o 






















CO 


CM 


rH 




















fa 










































60 




p 


















1 — 1 




1—1 


I — I 


















AA 


i— t 
















CO 


tH 


no 






















rt 


1—1 


a 








© 


o 


05 


o 


Mi 


r-l 


o 


*~ 


i-H 




















H 








CM 


o 


rH 


c^ 


CO 


r-l 


05 


•* 


M5 





















■< 


o 








CO 


■* 


CM 


o 


co 


£- 


■>* 


eo 


CM 


















3 


o 


fa 








rH 


rH 


i-H 


T-i 










































1 ' 


1 1 


i I 




1 1 


i 1 






























































O 
















CM 


CM 


m 






















-m 




»o 


t~ 


«5 


05 


CO 


05 


05 


Mi 


CO 


-* 






















O 




a 


o 


i-H 


© 


CM 


o 


i—* 


>o 


CO 


r-l 


05 
























© 


CM 


00 


CO 


■* 


CM 


o 


CO 


t~ 


•* 






















rt 




o 


CM 


CM 


rH 


rH 


rH 


rH 


rH 






i t 
























fa 










































rji 






















































































M5 






ID 

.a 




































co 


J^ 


CO 






a 

3 










05 


o 


«5 


05 


CO 


CO 


CM 


»o 


CO 


o 


o 


00 


CM 


•* 


rH 








»M 








CM 


o 


rH 


M5 


CO 


rH 


05 


■* 


•* 


CO 


i>. 


CO 


rH 


o 


© 






a 




o 








CO 


tH 


CM 


O 


oo 


t~ 


■* 


eo 


CM 


i-H 




























i— 1 


rH 


i-H 


rH 






















































■* 


eo 








J^ 


M5 


rH 


© 






i * 








o 


«5 


CO 


© 


r-l 


o 


■* 


o 


O 


o 


o 


o 


O 


© 


© 


© 


© 


o 
u 












© 


O 


o 


O 


© 


o 


o 


o 


o 


o 


o 


o 


o 


© 


© 


© 


© 




P CD 










+ 


+ 




+ 




1 




1 


1 








+ 


+ 


+ 




<3> 

J3 














































H 




M 
























M5 


1^ 


o 


CO 


o 


1^ 


Wl 


rH 


© 


* 




a 






















CO 


J>. 


rH 


00 


CO 


© 


CO 


05 


M5 


CM 


























eo 


O 


•* 


■* 


05 


■* 


r-i 


© 


© 


© 




rH 


o 
fa 






















»o 


"* 


CM 


I-H 
















w 
Q 














































<i 


mj 


© 


00 


M5 


CO 


05 


J>- 


CM 


CO 


CO 


CO 




rH 

CO 


















a 


lO 


CM 


•* 


o 


C5 


o 


tH 


■* 


i> 


r-l 


CO 


o 


tM 




















i^ 


tH 


rH 


05 


CO 


>o 


CO 


r-l 


05 


t» 


«s 


rh 


CM 




















o 

fa 


CM 


CM 


CM 




































































eo 








© 


oo 










«5 
© 


CO 
CO 


CO 

© 




r-l 


CO 


CD 
CM 


CO 

cb 


00 
O 


CM 


CO 


CO 
05 


© 


CO 
rH 


© 
© 


M5 
© 


CM 

© 






9 P.3 








05 


CO 


ms 


CO 


r-l 


05 


J>- 


>o 


^ 


CM 


i-H 


















H 








r-l 


rH 


i-H 


r-l 


r-l 




























g 


'd ,2 










































a 






.CO 


.© 




• CO 


.CO 




Mi 




























d a s 

"S '3 || 

(DO 11 

faP 




no 


© 


ms 


CO 


rH 




CM 


Mi 




«5 






















3D 


o 


o 


l-H 


CM 


CO 


■* 


M5 


CO 


£~ 


o 


CM 


M5 


o 


M5 


o 


© 


© 


© 


© 


© 




o 
g 

c 




o 


o 


O 


O 


o 


O 


o 


o 


I-l 


rH 


rH 


CM 


CM 


CO 


tH 


M5 


© 


i> 


oo 




T3 


■Ja 
o 








































O 




.s 














Mi 

































o 


r-i 


<M 


CO 


T* 


>o 


CO 


i> 


05 


o 


CO 


CO 


o 


CO 


o 


© 


© 


© 


© 


© 




rC fa 












































QQ 

s 


a 




















« 






4h 




£ 


« 


4! 


« 


4h 


eg 
























i-H 






CM 




CO 


Tji 


M5 


© 


.t- 


co 





VOL. XXIV. PART I. 



2 A 



86 PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 

69. The formulse used in the preceding calculations are the following :- 



Case I. < 



Case II. 



( /»% i i ~-e e -66184a; 

(A)Iog, = lo g 275-5- 1 + . 13()93j 

•3472~ 
(Bj log v = log 4-0+ 1 _. 05 Q 6g > where *=4-a 

(C) log „=log 2605- j^g- 
( D ).o g „=,o g 209-08 -jS"* 



Case III. 



•4217r 
(E) log « = log 0-47 + 1 _. 0405g . where ~ 



(F) log ,=W MM-fL^jj 



= 5 — x. 



(G) log*=log 052 + 



•4521* 
1--0282*' 



where ~ = 5 — x. 



70. With reference to the preceding numerical Table, I may remark, First, 
that the differences shown are not in all cases deviations from direct observations, 
but between the formulse and the graphical interpolation of the data. There is a 
difficulty (which will be understood from Art. 57) in comparing compendiously 
the formulse with the single data of Table I. When the points of the curve are 
somewhat distant from points of observation, the numbers in the preceding Table, 
obtained from the formulse, may be, and probably are more reliable than those 
assigned from the curve. Secondly, the curve of Case I. appears to be the most 
reliable in all respects. And in particular I consider the portion of the curve 
which includes the highest temperatures, or those corresponding to points on the 
bar between and 3 inches, to be very nearly accurate. From numerous inde- 
pendent calculations, I conclude that the value of v at the origin, or in contact 
with the crucible, is pretty exactly 275°5 Cent., as there assigned. If we add to 
this 12°-5 for the approximate temperature of the apartment, we have 288° for 
that of the bar where it enters the crucible, and is supposed to have very nearly 
the temperature of melting lead. This is a considerably lower temperature than 
is usually attributed to melting lead * 



* Usually stated at from 320° to 330° Cent., 608° to 626° Fahr. Biot, indeed, gives it as 
only 260°, inferentially derived from his conduction experiments (Traite de Physique, iv. 677) ; hut 
this is on the supposition of the logarithmic law prevailing. Crichton, junior, gives 606° 5 Fahr. 
(T. Thomson); Daniell, 612°; Kupffer, 633°. Supposing any of these last numbers to be correct, the 
inference must be, that in the conduction experiments described in the present paper, the temperature 
of melting lead did not extend to the outside of the iron crucible when the origin of the co-ordinates 
has been taken, but must be sought somewhere in the interior. This conclusion is strengthened by 
some otlier, though indirect considerations. 



THE LAWS OF CONDUCTION OF HEAT IN BARS. 87 

71. I cannot too distinctly repeat that the formulae adopted in the preceding 
Table are only to be regarded as a means of more conveniently grouping the 
observations. The most important use to be made of these formulae, however, 
yet remains to be mentioned. It will be seen by reference to Arts. 6, 28, &c, of the 
former part of this paper, or to § IV. of the present paper, that it is not the ordi- 
nates themselves of the statical curve of cooling which are to be used in obtaining 

the conductivity of the bar, but the values of the differential coefficient - ~ for 

each part of the bar. In other words, we must be able to draw a tangent to the 
curve of statical temperature at any point of the curve. This may be roughly 
done mechanically, or it may be done by dividing the curve into short elementary 
portions, and treating each portion as if it were part of a logarithmic curve (see 
below, Art. 82, on the Analogous Treatment of the Dynamical Curve) ; or, 
finally, it may be obtained from the equations above given. The two last methods 
have been used in the reductions, and especially the last of all, which is the only 
satisfactory one for the higher parts of the statical curve. The general form of 
the empirical equation being, 

Tab. log v = A ■ 



1 + CX 

when reduced to Napierian logarithms, gives 

7)7* 

0-4343 hyp. log v= A 



1 + ex 



and ?= -2-3036, 



dx (1 + ex) 2 

whence the numbers which will be given in § IV. of the present paper are com- 
puted, the values of b and c being taken from the formulas of Art. 69. 

§ II. Experiments on Cooling. 

72. The Apparatus. — It will be seen, by reference to the former part of this 
paper (Arts. 5, 24), that, in order to interpret the indications of the permanent 
temperature of a bar, and to deduce its conductivity, we must have an inde- 
pendent set of observations on the cooling of a similar bar, or a portion of a 
similar bar. For this purpose, the apparatus shown in fig. 2 of Plate I. was 
employed. The same short bar, L M, which has been already referred to (Art. 
51), as being used in the statical experiment for determining the temperature 
the bar would have had independently of the heat applied at one end, was sup- 
ported on the props N, 0, after being duly heated. It is now to be used to ascer- 
tain the rate of loss of heat from a bar having the Section and Surface proper 
to each of the three Cases of Art. 48, in terms of the scale of the thermometer P, 
inserted at or near its middle point. 

73. I have so fully described, in Art. 24, the manner of performing the 



88 PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 

Cooling experiment, that I need here do little more than refer to the figures by 
which it is now illustrated, and give the corrected results as to the " law of cooling.*' 

74. Fig. 2 of Plate I. shows the small iron bar employed, which in Case I. and 
Case II. (Art 48.) was 20 inches long and 1} inch square, first naked and 
polished, and afterwards covered with paper ; it was marked C. In Case III. it 
was a polished (or at least a bright) bar, 20 inches long, 1 inch square, and 
marked E. Each bar had a ring at each end, /, to, and could be handled by 
seizing either end by the hook Q, fig. 3. Having been covered with several folds 
of stout paper to prevent a sudden chill of the metal bath into which it was to 
be introduced, it was lowered vertically and lengthwise into the cylindrical iron 
vessel shown at fig. 3, and in section in Plate II. fig. 2. It consists of a stout iron 
tube T V, about two feet long, with a bottom at V, and a handle at T. It rests 
by means of two iron pins, o, p, on the upper edge of a cylindrical iron chimney 
R S, supported by three feet, of which two are seen at q and r over the gas fur- 
nace U, the powerful flame of which, playing between the two cylinders, keeps a 
quantity of solder or of " fusible metal" in the interior one, not only melted, but 
heated considerably above the melting point. The bar under experiment, after 
being coated with several folds of paper, having usually also been well warmed 
over a hot-air stove, was introduced by the hook Q into the metal bath, then turned 
end for end several times, until it was believed that the heat had well penetrated 
its entire thickness. It was then withdrawn, shaken, the paper covering rapidly 
cut off, the bar wiped with a cloth,* and placed horizontally on the two ivory- 
topped props N, (Plate I. fig. 2), the thermometer P inserted in the central 
hole,f into which heated mercury had already been placed, and the reading of* 
the thermometer from minute to minute immediately commenced, the times 
being given by an assistant. The free temperature was determined by a ther- 
mometer sunk in a cold bar in the neighbourhood, or by one suspended in the 
air, or by both. 

75. The Observations. — As in the statical observations there are three cases. 

Case I. Iron bar, 1 } inch square, roughly polished. 
Case II. Do. do. covered with paper. 

Case III. Do. 1 inch square, roughly polished. 

76. Two independent sets of observations of the law of cooling on different days 
have been obtained for each case. Moreover, as more than one thermometer was 
observed in the holes of each bar (as in the example which follows), except for the 
very highest temperatures, use has from time to time been made of these auxiliar} r 
series. The whole of these observations have been most carefully corrected for the 

* The wiping of the bar I believe to have been unnecessary and injurious. It lowered the 
temperature, and interfered with the distribution of the heat in the bar. 

| The 1^ inch bar had a central hole, and others 1*5 inch distant, right and left. The 1 inch 
bar had only two holes equidistant from the centre of the bar. 



THE LAWS OF CONDUCTION OF HEAT IN BARS. 



89 



scale errors and for the temperature of the stem. Where the temperature of the air 
of the room has not been quite steady, the variations have been interpolated and al- 
lowed for in deducing the excess of temperature of the bar above that of the room. 
77. I shall give the details of one experiment as a specimen (all reductions 
being first made). 



TABLE IV.— Cooling of Short 11-inch Bar, C.— 26th March 1851. 





Hole (2), 


Hole (1), 


Hole (3), 




Hole (2), 


Hole (1), 


Hole (3), 


Hour. 


Centre. 


to the Left. 


to the Eight. 


Hour. 


Centre. 


to the Left. 


to the Eight. 


Corrected 


Corrected 


Corrected 


Corrected 


Corrected 


Corrected 




Excess. 


Excess. 


Excess. 




Excess. 


Excess. 


Excess. 


h. m. s. 





o 





h. m. s. 





o 


o 


12 59 


170-7 






2 1 




55-20 




1 


1674 






2 


5415 






1 


164-0 






3 






53-2 


2 


16085 






4 


52-4 






3 


157-6 






5 




51-65 




4 


1545 






6 


50-6 






5 


151-45 






7 






4975 


6 


14845 






8 
9 


490 


48-35 












12 
13 


131-7 
129-2 






10 


47 -4 














14 


126-6 






21 


40-1 


40-15 




15 


124-2 






22 


39-35 




39-40 


16 


121-7 


119-85 




24 


38-25 


38-20 




17 








26 


37-10 




37-10 


18 
19 
20 


116-95 
112-65 




114-25 


28 


36-0 


3605 




48 
50 


269 
26-15 


26-95 


26-2 


21 
22 


108-35 


110-85 




52 

54 


25-4 
24-6 


25-4 


24-6 


23 






106-0 










24 


104-5 




3 31 


14-95 


14-92 




25 




10305 




34 


14-35 


14-32 




26 


100-65 






36 

38 30 


14-0 
13-40 




13-92 
13-25 


29 






95-10 














30 


93-75 






4 10 


8-98 


9-00 


8-92 


31 




92-05 




15 


8-48 


8-50 


841 


32 


90-25 






20 


798 


79 


7-8 


33 
34 


87-0 


88-9 




25 


753 


7-55 


7-44 










35 






85-5 


6 0* 


2-79 


2-6 




36 


84-10 






10* 


2-54 


2-4 




37 






82-5 


20* 


2-15 


2-1 




38 

39 


81-25 


79-95 




30* 


2-0 


1-9 










40 


78-50 






8 10* 
20* 


0-9 
0-9 


0-7 
0-7 








2 


56-10 






30* 


0-85 


0-7 




* Rea 


d by an assi 


stant. The 


scale of the 


thermometer 


in hole (3) 


being liable 


to mistake 


in reading 


its results t 


ire omitted. 













VOL. XXIV. PAET I. 



2B 



90 



PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 



78. Graphical Interpolations. — The observed excesses of temperature (as ob- 
tained, for example, in the preceding experiment for the central hole) were pro- 
jected in a curve of which the times were taken as abscissie, and the independent 
temperatures of the bar as ordinates. When more than one series of observations 
(on the same bar at different times) were to be combined, a procedure exactly 
similar to that described in Art. 57 for the stationary temperatures was emplo}'ed ; 
that is to say, one series being first projected on the engraved paper as funda- 
mental, any other series was next similarly projected on tracing cloth, and the 
system of points thus obtained was moved to the right or left over the first, until 
the points in the two curves appeared to be superposed satisfactorily. The inter- 
polated observations were then pricked through, and a curve drawn through 
the whole. 

TABLE V. — Curves op Cooling (in Terms of Time). 



Time from 


■ E I. 


Cask II. 

1J inch Bar, 

covered. 


III. 


Arbitrary Origin. 


1^ inch Bar. 


1 inch liar. 




March 26. 


b 29. 






-10 Min. 


... 


; 242-3 






- 5 


, m 




*221-4 


*263-9 


... 


- 2-5 






*2ll-5 


*243-6 


. . . 









*201-9 


"225-0 


"258-5 


2-5 






1920 


*207-7 


243-3 


5 






1835 


*191-8 


-2289 


7-5 






1748 


177-0 


*215-3 


10 


1673 


166-5 


163-6 


202 4 


12-5 


159-1 


158 2 


150-6 


190-05 


15 


151-4 


150-6 


1391 


178-7 


20 


1370 


1365 


119-25 


15755 


25 


124-2 


124-2 


10295 


138-9 


30 


1126 


112-8 


88-8 


122-45 


35 

40 


102 6 


1025 


771 
670 


108-6 
96-45 


93 7 


50 


786 


50-95 


77-25 


60 


65-9 


39-4 


62-2 


70 


55-8 


30-65 


50-5 


80 


47-3 


24-25 


41-3 


90 


40-5 


19-2 


33-95 


100 


34-9 


15-27 


28-2 


125 


242 


8-9 


180 


150 


171 


5-45 


11-95 


175 


123 


3-42 


81 


200 


8 95 


2-15 


5-55 


300 


2-95 


0-4 


1-4 


400 


1-12 




0-4 


The number* 


5 marked thus * are deduced frc 


m the Equation 


s of Art. 88. 



THE LAWS OF CONDUCTION OF HEAT IN BARS. 91 

79. A specimen of the Curves of Cooling is given in Plate IV. The subsidiary 
curves in the same plate show different sections of the main curve projected on 
different scales (as in the case of the Statical Curves, Art. 60), for convenience of 
interpolation. The main curve corresponds to Case I. The dotted line adjacent 
to the main curve in the Plate shows the modification of the law of cooling 
introduced by covering the bar with paper, as in Case II. The results of the 
whole are shown in the preceding Table. The origin of the abscissae (the times) 
is of course wholly arbitrary in each case. 

80. The continuity of the curves thus obtained was in general satisfactory, 
though in one or two instances it seemed desirable to project part of two curves 
as distinct, as in Case I. 

81. It is of little use, however, to possess merely a knowledge of the free tem- 
perature of the bar in terms of the time. The valuable information which we 
require in the deduction of conductivity is the " rate of cooling," or the pro- 
portional momentary loss of heat corresponding to a given excess of tempera- 

sjy 

ture. This is expressed mathematically by -j, and might be directly obtained by 

discovering the equation to the primary curve of cooling, and then differen- 
tiating it. 

82. There is, however, not less difficulty in finding a formula of interpolation to 
represent the curve of Cooling throughout its extent, than we have already found 
in the case of the curve of Statical Temperature, and it would evidently require the 
introduction of as many constants. I therefore preferred, in the first instance, 
(seeing that from the multiplied observations of cooling, the ordinates of this curve 
are more perfectly known than in the other case), to subdivide it into elementary 
arcs, and treating each of these as a portion of a logarithmic curve (to which it 

approximates), to find the value of ^-, or the " rate of cooling," corresponding to 

successive values of %* and by projecting these in curves to study their inflections 
in detail in each of the three forms of experiment already often referred to. 

83. The three upper figures of Plate V. represent the " rates of cooling" of each 
bar in terms of its temperature-excess. From the study of these the peculiarities 
of the law of cooling above adverted to will become evident, and the harmony 
of the three cases is exhibited to the eye. 

84. First, For very small excesses of temperature, the rate of cooling is com- 
paratively slow, but increases much more rapidly than the temperature. To illus- 

dv log v — log v v' + v 
f By the formula — = 2-3026 — -, x — - — , where v and v' are the excesses of tempera- 

Civ h — Lt 

v' + V . 
ture corresponding to the times t and t' . — — is the mean ordinate to which the result corresponds. 

The logarithms are tabular. 



92 PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 

trate this, a portion of each curve near its origin has been drawn separately on 
an exaggerated scale in a subsidiary figure, where its deviation from a straight 
line is abundantly manifest. In each case it may be adequately represented for 
the first 4° or 5° by an arc of a common parabola — more accurately perhaps 
by a semicubical parabola. However, taking the former as the simplest, I 
find the following equations to represent the part of the three curves nearest 
their origin : — 



*o' 



Case I. ~ = -00830 v + 000615 v 2 
at 

Case II d ^ = 01626 v + 00065*/ 2 
at 

Case III. ^ = -01046 v + -00091 v°- 
dt 

85. Secondly, The concavity upwards of these curves of the " rate of cooling" — 
showing that the cooling increases faster than the temperature rises— gradually 
diminishes; and in all the three curves we find between 110° and 120° (centigrade), 
a space nearly straight, indicating a point of contrary flexure. Above 1 50' the 
curve is in all the three cases slightly convex upwards, showing a rate of cooling 
slower in proportion than the rise of temperature. 

86. Thirdly, This last circumstance appeared to me to be deserving of an 
elaborate verification. , I therefore applied the same formula of interpolation 
which I had used with success to represent considerable arcs of the statical curve 
of temperature (see Art. 67, Eq. (1.) ), being what has been called Roche's formula, 
to represent the temperatures of the cooling bar in the higher parts of the pri- 
mary curve of cooling. 

87. In this I was successful, and I deem the matter of sufficient importance 
to show the coincidence between the original thermometric observations and the 
formulae employed in each of the three cases. The times (t) are in each case 
reckoned from an arbitrary origin ; and v is the excess of temperature above that 
of the air actually observed. [See Table VI.] 

88. Fourthly, It will be seen that, within the limits of these tables, the obser- 
vations are, upon the whole, well represented by the equations. Moreover, they 
confirm a result at which I had previously arrived from the projections, as to the 
law of cooling at higher temperatures, namely, that above 140° or 150° there 
is a gradual falling off in the rate of cooling, compared to the measure of tem- 
perature. For it is to be observed, that the equations employed to represent 
the primary curve of cooling coincide with the simple geometrical or logarithmic 
law, when the co-efficient of t in the. denominator of the fraction (c of Art. 67) 
vanishes. When this co-efficient is positive, the progression is faster than geome- 
trical ; when negative, it is slower. Now, in each of the three cases c is negative, 



THE LAWS OF CONDUCTION OF HEAT IN BARS. 



93 



TABLE VI. 



Case I. 


— 1^-inch Bar, Naked. 


Case II 


. — 1|-in.Bar, Covered. 


Case III. — 1-inch Bar, Naked. 




Formula ; 




Formula ; 


Formula ; 


log V = 


„,„,„. -008133* 
= 2 ' 304 ' 1 1-0026*' 


log V- 


= 2 35215 


•01385* 
1_-00007«' 


. O/IIOKK -0105K 

log, = 241255 ^mw 


t 


V 

observed. 


v calc. 


Diff. 


t 


V 

observed. 


v calc. 


Diff. 




observed. 


v calc. 


Diff. 


minutes. 





» 





minutes. 


o 





O 


minutes. 


o 








2-5 


1921 


192-45 


+ 0-35 


7-5 


177-0* 


1771 


+ 0-1 


9 


207-4 ; 207-5 


+ 0-1 


3 


190-3 


190-55 


+ 0-25 


8 


174-3 


174-3 


00 


10 


202-4 202-4 


0-0 


4 


187-15 


187'0 


-015 


9 


168-7 


1688 


+ 0-1 


11 


19745 197-4 


-0-05 


5 


183-5* 


183-45 


-005 


10 


163-6 


163-5 


-01 


12 


192-65 192-6 


-0-05 


6 


17995 


179-95 


00 


11 


158-25 


1584 


+ 0-15 


13 


1879 1879 


00 


7 


176-55 


176-55 


00 


12 


153-4 


153-4 


00 


14 


183-25 183-3 


+ 0-05 


8 


173-1 


173-15 


+ 0-05 


13 


148-4 


148-5 


+ 01 


15 


178-7 


178-7 


0-0 


9 


1697 


169-65 


-0-05 


14 


143-75 


144-0 


+ 0-25 


17-5 


167-5* 


167-8 


+ 0-3 


10 


166-55 


166-4 


-015 


15 


139-3 


1393 


0-0 


20 


157-55 


157-55 


00 


14 


153 45 


153-7 


+ 0-25 


16 


135-0 


135-0 


0-0 


21 


153-75 


153-5 


-0-25 


15 


150-45 


150-55 


+ 0-1 


17 


130-9 


130-8 


-01 


22 


149-9 


149-7 


-0-2 


16 


147-65 


1475 


-015 










23 

25 


146-1 
138-9* 


146-0 
138-7 


-01 

-0-2 


* Fro 


m interpolating curve. 




* Fron 


i curve. 


* From curve. 



consequently the progression is slower than geometrical, and the curve of the 
" rate of cooling," in terms of v, is convex upwards, as already stated. 

89. Fifthly, By satisfying the observations by equations, we have farther these 
advantages — (1.) We can, with approximate accuracy, extend the law of cooling 
somewhat beyond the limits of observation, though with caution ; (2.) We can also 

obtain the values of -r in a ready and continuous manner. The higher parts of 

the curves in Plate V- have been deduced in this way, and thus the " rate of 
cooling 1 ' has been tabulated for temperatures higher than those actually observed ; 
but such numbers, being more or less hypothetical, are distinguished by asterisks 
in the following Table, which in other respects includes the results obtained from 
the observations treated as has been already described. 



VOL. xxiv. PART I. 



2c 



94 



PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 



civ 
TABLE VII. — Showing the " Rate op Cooling,"—^- for Different Excesses of 

at 

Temperature (y). 





Case I. 


Case II. 




Case III. 




V. 


1J inch Bar, 


1J inch Bar, 


Ratio to I. 


1 inch Bar, 


Ratio to I. 




naked. 


papered. 




naked. 




1 


0009 


•017 


1 


00115 


- 


2 


•019 


•035 


► 174 


•0245 




3 


031 


•054 


0395 


1-28 


4 


•043 


•075 




056 




5 


•057 


•096 


> 


•072 


, 


10 


0124 


•203 


1-64 


•158 


1-27 


20 


•275 


•44 


1-60 


•34 


1-24 


30 


•43 


•72 


1-67 


•55 


1-28 


40 


•60 


1-01 


1-68 


78 


1-30 


50 


•80 


1-30 


1 62 


101 


1-26 


60 


101 


1-62 


1-60 


1-25 


124 


70 


1-21 


1-95 


1-61 


1-52 


1-26 


80 


1-42 


227 


1-60 


177 


1-25 


90 


L63 


260 


1-59 


2-04 


1'25 


100 


1-84 


2-95 


1-60 


233 


1-27 


120 


2-27 


367 


1-62 


2-92 


1-28 


140 


2-80 


4-40 


1-57 


3-50 


125 


160 


318 


508 


1-60 


4-03 


1-27 


180 


348 


5-75 


165 


4-50 


1-29 


200 


3-78 


*6-38 


1-69 


4-95 


1 31 


220 


*4-04 


*7-00 


173 


5-40 


1-34 


240 


*429 


*765 


178 


*5-85 


1-36 


260 


*4-52 


*8-28 


1-83 


*6-30 


1-39 


280 


*4-75 


*8-90 


1-88 


*672 


1-42 


The num 


bers marked thus * being the results of calculation, are to be regarded as 


more or less h 


ypothetical, and increasingly so at the higher temperatures. 



90. Sixthly, I will not attempt to account for the inflections of the curves of 
Plate V. on physical principles, farther than to remark that the rapid increase in 
the velocity of cooling with temperature in the lowest part of the scale is perhaps 
owing to the separate effects of cooling by radiation, and cooling by convection. 
It seems probable that a certain excess of temperature of the bar above the air is 
necessary to determine efficient atmospheric currents, and thus to accelerate the 
rate of cooling ; that, in fact, there is an amount of viscosity in air, which it re- 
quires a certain elevation of temperature properly to overcome. I would also 
observe, that the cooling in Case I. is (at higher temperatures) less regular than 
in the two other cases, while in Case III. the logarithmic law is almost accurately 
observed at those temperatures. This is no doubt to be ascribed to the greater 
mass of the Bar No. L, compared to its radiating power, occasioning probably 



THE LAWS OF CONDUCTION OF HEAT IN BARS. 95 

sensible irregularities, depending on the primitive distribution of heat in the bar, 
and on the want of uniformity in the temperature of its transverse section. The 
nearer that we approach to the ideal of an infinitely slender bar, the more shall 
we escape those periodical irregularities (see Art. 25 of the former part of this 
paper), arising from the primitive distribution of heat in its substance, which no 
doubt gives rise to some of the peculiarities of the inflections in the curves 
of " rates of cooling." In particular, we may naturally ascribe, in part at 
least, to the fact that the bar is heated first of all to a uniform temperature 
throughout in the fusible metal bath, the relatively diminished rate of cooling 
observed at the highest temperatures. At the same time I would repeat the 
caution, that the hypothetical or dotted portion of those curves cannot be relied 
on as expressing an actual fact, at least to more than a little way beyond the 
range of experiment. 

§ III. On the Proportion of Heat dissipated from the Bar by Radiation and Convection. 

91. Although not of direct importance to the determination of conducting 
power, I will indicate shortly how the numbers in Table VII., may be used to 
ascertain the relative amount of heat lost by radiation and convection at any or 
all points of the surface of the bar in Cases I. and II. The method was originally 
due to Sir John Leslie, but was stated more clearly by Dalton (System of 
Chem. Philosophy, p. 115), and was happily applied by Dulong and Petit. 
Suppose the total " rate of cooling" of the same bar to be ascertained in air, first. 
when it is naked, and, secondly, when covered with paper, and let the ratio of 
the first case to the second be as 1 : p. Next, by comparing after the manner of 
Leslie's canister-experiments the " emissive power" of the same two surfaces, 
iron and paper, let it be as 1 : q. Let the required ratio of the heat lost by con- 
vection to that lost by radiation be as 1 : x in the first case ; then, of course, it 
will be in the proportion of 1 : qx in the second. But as the heat dissipated in 
each case is the sum of the effects due to convection (which is always = 1), and 
that due to radiation, we have 



and 



1 : p — \ + x : 1 + qx 

p-1 

x = 

9—P 



92. I have given in Table VII. the ratios of cooling, at different temperatures, for 
Cases I. and II. , that is, for the same bar covered with paper and naked iron ; 
and though the ratios vary somewhat,* yet they agree pretty nearly within the 

* Since this was written, I have observed that a like diminution of the ratios of cooling from glass 
and silver up to a certain point, and afterwards an increase, was noticed .by Dulong and Petit, in 
their admirable Memoir on the Law of Cooling, page 102. — Mem. Acad. Sci. Par. 



96 PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 

safe limits of observation. In fact, if we compare the average ratio froml 0° to 
100° Cent., and again from 100° to 200° Cent., we shall find them to be almost 
identical. They give for the value of p, the number 1 6023. This represents the 
proportion in which the papered bar dissipates its heat more rapidly than the 
naked bar. 

93. For the direct radiating or emissive power of the two surfaces, I had re- 
course to the kind aid of Mr Balfour Stewart, not having had recently con- 
veniences for making the experiment myself. He used the thermo-electric pile, and 
he found the experiment to be attended with considerably greater difficulty than is 
commonly attributed to it. I believe that Mr Stewart is not yet satisfied as to 
the reliability of his methods of observation ; but the four best series of experi- 
ments made in February and March 1864, gave the emissive power of paper 
compared to iron as 5*8 to 1.* The value of q is therefore 5-8. 

94. Hence by the previous investigation — 

The value of x, the heat dissipated by radiation from naked iron (the dissipation 
by convection being always =1) is ^ = 5T g- ro60 = 0-116. In the case of the paper 

surface, x is 58 times greater, or = 673. In other words, of the heat dissipated 
from the bar in Case I., nearly T 9 ths are lost by convection, and ^th by radia- 
tion. In the paper-covered bar (Case II.;, only T %ths are lost by convection, and 
3*0 ths by radiation. f 

95. From this it appears that the principal agent in the dissipation of heat in 
these experiments is Convection and not Radiation ; nay, that the effect of the 
latter is comparatively almost insensible, when naked metallic bars are used. 
This of itself tends to explain the systematic deviation of the statical curve of 
temperature (Art. 64) from the logarithmic law. The experiments of Dulong 
and Petit show that the dissipation of heat due to Convection increases not as 
the excess of temperature simply, but as its fth power nearly (more exact! v 
1-233). This accords so far with what has been said of the variation in the rate of 
cooling in Art. 84 ; but it gives no adequate explanation of the inflections of the 
curves of Plate V. at higher temperatures. Were it not for the unquestionable 
precision of Dulong's admirable experiments, in which the law of cooling due 
to the contact of air was verified as high as 260° Cent., one might have not un- 
reasonably supposed that the energy of convection was relatively less at higher 
temperatures. 

* This corresponds nearly to the relative emissive power of glass and polished silver used bv 
Dulong. 

\ For in Case I. the whole heat lost from a point having a given temperature being represented 
by the number I'll 6, that due to Convection is 1, that due to Radiation is -116. In Case II. the 
total loss is 1673, whereof 1 is due to Convection, and 673 to Radiation. 



THE LAWS OF CONDUCTION OF HEAT IN BARS. 



97 



§ IV. — The " Statical Curve of Cooling" Becapitulation and Application of the Method 

of Deducing the Conductivity. 

96. It will be convenient here to recapitulate, from Arts. 5, &c. of the former 
part of this paper, the use which is to be made of the data obtained from the two 
fundamental experiments described in the previous sections, namely, the deter- 
mination of the Curve of Statical Temperatures (Table II. Art. 61), and the rate 
or velocity of Cooling of the bar at any temperature (Table VII. Art. 89). 

97. Let A B be the bar, kept hot at the extremity A, and left to assume a per- 




manent temperature at its various points under natural causes. Let the upper 
curve, or DFE, represent by its ordinates (as FC) these temperatures. All the 
heat that enters the bar at A, and is propagated along it, has to be accounted for. 
Since the bar is so long that at the end B the heat has become insensible, the 
entire heat entering the bar at A has been dissipated from its surface in various 
proportions, according to its temperature, between the point A and some remote 
point E where the elevation of temperature is practically insensible. In like 
manner, if we take any point C in the bar, the heat transmitted from the hotter 
end, by conduction across the transverse section of the bar at C, is dissipated 
by the cooling of the bar between C and E. To know the quantity of heat 
passing across this transverse section, we have therefore to ascertain the aggre- 
gate loss of heat from the surface of the bar to the right hand of C. 

98. To do this, we must construct what I call the Statical Curve of Cooling, 
which is represented in the same figure by the curve LHM, beneath the bar AB. 
The ordinate C'H represents the heat lost by the bar per minute, from the portion 
CC, whose temperature is represented by CF in the upper curve. This loss or C'H, 
is found from Table VII., by entering it with the thermometer reading CF, which 
again is known from Table II. in terms of the position of the point C in the length 
of the bar. Thus all the ordinates of the Statical Curve of Cooling, LHM, can 

VOL. XXIV. PAET I. 2D 



98 



PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 



be constructed. Dividing the length of the bar into sections, in the three experi- 
mental cases so often referred to, the ordinates of the curve of statical cooling, or 



dv 



values of — j-, appropriate to every point of the bar, will be found as in the 
following Table: — 



TABLE VIII. — Showing the Rate of Cooling proper to each Point of the Length 
of the Bar (or Ordinates of the Statical Curve of Cooling) , containing also the 

dv 



VALUES OF — 



dx 



Distance from Origin 
in Feet and Inches. 


Case I. 


Case II. 


Case III. 


dv 
dl 


dv 
dz 


dv 
dt 


dv 
dx 


dv 
dl 


dv 

dz 


Ft. In. 

„ o 

„ 1 
„ 2 
„ 3 
» 4 
„ 5 
„ 6 
„ 7-5 
„ 9 
I. 
6 
II. 

III. 

IV. 
VI. 


o 

4-71 

4-32 

3-97 

3-64 

332 

301 

2-70 

2-20 

1-80 

1-245 

0-620 

0-342 

0114 

0043 

0008 


O 

420 
362 
314 
272 
237 
2068 
1810 
1488 
1230 
85-35 
43-70 
2447 
815 
334 
0-57 


O 

830 

706 

605 

5-20 

4-41 

3-73 

314 

2-48 

1-98 

1-28 

0-58 

0-282 

0070 

0021 


O 

512 
423 
351 
292 
245 
206-5 
1752 
1376 
1090 
699 
35-2 
163 
4-47 
1 36 


o 

6-75 

5-92 

519 

4-54 

400 

344 

293 

233 

1-85 

1185 

055 

0-258 

0070 

00185 


o 

512 

432 

366 

310 

264 

226 

1936 

1546 

1241 
81-6 
380 
1964 
5-52 
169 


dv 

N.B. — The values of —-r are computed by the method explained in Art. 71. Only 

at some of the lower temperatures a mixed method of calculation and projection has been 
used. 



09. It is evident that, if we can effect the quadrature of successive sections of 
the statical curve of cooling, continued until it vanishes in the direction of the 
cool end of the bar, we shall have got the " flux of heat" across the section of the 
bar at which the quadrature commences. The measure of the heat expressed by 
the area of the curve in question will have for unit the amount of heat required 
to raise unit of volume (1 cubic foot) of iron by 1° Cent. The shaded curve, 
in the lower part of Plate III., shows the Statical Curve of Cooling proper to 
Case I. The ordinates of the curve are related to those of the curve of statical 

temperature immediately above it, by the relation of — y to v, shown in the 

secondary curve of cooling in the upper figure of Plate V. 



THE LAWS OF CONDUCTION OF HEAT IN BARS. 



99 



100. The flux of heat is greatest in the hottest part of the bar, because the 
temperature of the bar varies most rapidly there, and the heat is more rapidly 
drawn towards the cold end. To give exact expression to the tendency of the 




heat to traverse the section of the bar at C, we will take Cc to represent the 
thickness of a plate, bounded by imaginary parallel surfaces, situated transversely 
within the bar through which the flow of heat is to be considered. This is to 
be compared with the flow of heat across any other plate, Gg, of equal thickness, 
in a different part of the bar. Then, according to Fourier, the flow of heat 
across Cc will be proportional to the small decrement of temperature F$, by 
which the side of the plate nearest to A is hotter than the farther side, and to 
the Conductivity jointly. The value of this decrement, F$, is evidently nothing 

else than the differential coefficient -r-, which has been given in the last Table, as 

derived from the equations to the curve of statical temperature in Art. 71. 

101. Hence (in conformity with Arts. 7, 31, and 35 of the first part of this 
paper), 

dv 



Flux of heat, or area CFE = — — x conductivity, 

dx 



or 



Conductivity 



Area CFE 

dv 

dx 



§ V. — The Method of this paper applied, under the usual assumptions made in the Theory 
of Conduction, as a first approximation to the determination of Conductivity. 

102. The area of the statical curve of cooling to the right hand of any ordi- 
nate is therefore to be found. It will be convenient, for this purpose, to show 
what the nature of this curve would be were theusual assumptions of the mathe- 
matical theory of Heat adopted. These assumptions are (1.) That the superficial 



100 PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 

loss of heat follows Newton's law, or that the loss of heat in unit of time varies 
simply as the excess of temperature ; (2.) That the same law holds for the internal 
communication of heat, or that the quantity of heat conducted is proportional 
simply to the difference of temperature of two adjacent elementary portions of 
a bar. 

103. From the first assumption it follows, of course, that the temperature of 
a cooling body of small dimensions varies in a decreasing geometrical progression 
with the time. The dynamical Curve of Cooling on this assumption is a 
logarithmic curve, t and v being the variables. 

104. From the second assumption, taken along with the first, we learn from a 
well-known analysis, that what we have called the Curve of Statical Temperature 
is also a logarithmic, x and v being the variables. 

105. Now the Statical Curve of Cooling (-r, in terms of x) must, on these as- 
sumptions, be also logarithmic ; for its ordinates — the velocities of cooling — are 
everywhere proportional to the temperature. Hence also the subtangent to 
these two last curves* is the same. Let it be M. Then by a property of the 
logarithmic curve (M being the modulus) the area of the curve bounded by an 
ordinate y, and carried to infinity, is My. Also the flux of heat corresponding 
to the position of the ordinate y is (Art. 99)= My, y being, as we have seen, 

= — y. But, by Art. 102, — -r is everywhere assumed (for the present) to be 

dv 

proportional to v, or — j =pv. Also since the dynamical curve of cooling is a 
logarithmic (103), let its modulus be m. Then, by the property of the curve, 
~ dt = m' Hence, comparing the last two equations p = — . And, 
F = Flux of heat = My = -M^ = M- 

^ at m 

and (by Art. 101). 

Conductivity = -j- = -r 

J dv dv 

dx dx 



But the curve of statical temperature being also assumed to be logarithmic (104); 
and consequen 
we finally get 



and consequently - -^ = =^; 



Mv M 2 
Conductivity = = — 

J m v m 

' M 

106. A first approximation to the conductivity of the bar may therefore be 
found by dividing the square of the modulus or subtangent of the statical curve of 

* Namely, the Curve of Statical Temperature and the Statical Curve of Cooling, being the two 
curves shown in the wood-cut of last page. 






THE LAWS OF CONDUCTION OF HEAT IN BARS. 101 

Temperature (assumed to be logarithmic) by the modulus of the Dynamical Curve 
of Cooling. 

107. Thus, to illustrate this by a numerical example, were we to attempt to 
reduce the statical curves of temperature of Table II. to logarithmics after the 
manner of Biot, we should probably find the following approximate values of the 



subtangent M : — 










Case I. 


Case II. 


Case III 


M 


0-9 foot 


07 foot 


0-8 foot 



And from Table V. of the Dynamical Curves of Cooling, the subtangents might 
be nearly 

m 60 min. 40 min. 50 min. 

whence 

— 0135 0122 -0128 

m 

which, it is seen, give nearly approaching values of the conductivity. 

§ VI. Final Determinations of the Conductivity of Iron at various Temperatures. 

108. The results given in the last section are in the' highest degree rude, and 
are introduced merely to illustrate the general form of the method. The curves of 
Temperature and Cooling are neither of them sensibly logarithmic, and therefore 
we have found the necessity of dividing them into small portions, and taking their 
elements from point to point. Therefore, in continuation of what has been said 
in Art. 99, we must proceed to the quadrature of the Statical Curve of Cooling 
whose elements are given in Table VIII. This is a curve which though not 
logarithmic, may, like the other curves we have already discussed, be treated as if 
it had been, when divided into numerous elements bounded by parallel ordinates. 
Every one of these segments may have its area estimated by the simple formula 
proper to a logarithmic curve,* and for the infinite branch a similar formula must 
be adopted. 

109. The following Tables contain the determination of the total Flux of Heat 
(F) across any section of the bar by the summation of the areas of the statical curve 
of cooling, commencing from the colder end of the bar, where this curve is (like 
the primary curve of temperatures) apparently asymptotic. In these Tables 
(corresponding to the three experimental Cases discussed in this Memoir, the chief 
uncertainty attaches to the two extremities of the curve. There are difficulties in- 
herent in the precise determination of very small excesses of temperature of a bar, 
whether in a statical or a cooling condition, above the surrounding air, itself not 
absolutely constant in temperature. These difficulties have been previously referred 
to. Moreover, when we have to take the ratio of two quantities, both to be experi- 

* Namely, area between ordinates y and ?/' = M (y'—y) where M the subtangent equals 

0-4343 &c. (x -so') 
log y' -logy 
VOL. XXIV. PART I. 2 E 



102 



PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 



mentally determined, and both in an almost evanescent state (as is the case in the 
extreme portion of the curve of statical temperature and of the statical curve 
of cooling), the quotient may be sensibly in error. To this I add, that in Case I. 
the length of the bar was certainly not quite sufficient to allow the conducted 
heat to be entirely spent by dissipation. Consequently there is, as it were, a 
slight congestion of heat towards the extremity — very slight indeed, but still 
sufficient to give to the subtangent there a too large value, and consequently to 
the decrement of the primary curve of temperature too small a one. Hence the 

Z 
ratio dv_ is somewhat too great, both in consequence of the numerator being too 
dx 

large and the denominator too small. But how little any such ambiguity can 

effect the general evaluation of the flux of heat in the succeeding lines of the Table, 

either in the case of this or of the two succeeding experiments, will be seen by 

noticing the minuteness of the areas representing the flux which correspond to 

the extreme portions of the curves. They are so small, that an error amounting 

to one-half their amount, would hardly affect by ^oth or 4-J^th part the measure 

of the conductivity in the middle and more important part of the Tables. 



TABLE IX. — Case I. I^-inch Iron Bar, Naked. Calculation of Area of Statical 
Curve of Cooling (F), and of the Conductivity at Different Temperatures. 



Limits of Abscissas. 


Limits of Ordinates. 


M=Sub- 
tangent.* 


Area 
M(y'-y). 


Total 

Area 

F. 


dv 

~Tx 


Conduc- 
tivity, 
F. 
dv 


Corre- 
sponding 
Actual 
Temp. 
Cent. 










X. 


%' . 


y- 


y'- 










~Tx 


(»+13). 


Ft. Inch. 


Ft. Inch. 


O 







j 








00 


VI. 


o- 


0008 


1-662 


0-0133 








VI. 


IV. 


•008 


•043 


1189 


•0416 00549 


3 34f 


•0164 


17 


IV. 


III. 


•043 


•114 


1-026 


•0728 


•1277 


8-15-j- 


0157 


22 


III. 


II. 


•114 


•342 


•9104 


•2075 


•3352 


24-47 


•0137 


37 


II. 


I. 6 


•342 


•620 


•8403 


•2336 


•5688 


■ 43-7 


•0130 


53 


I. 6 


I. 


•62 


1-245 


•7175 


•4484 


1-0172 


85-35 


•0119 


85 


I. 


9 


1-245 


1-80 


•6777 


•3762 


1-3934 


1230 


•0113 


110 


9 


„ 7-5 


1-80 


220 


•6233 


•2493 


1-6427 


1488 


•0110 


127 


„ 7-5 


„ 6 


2-20 


270 


•6100 


•3050 


1-9477 


181-0 


•0107 


147 


„ 6 


,, 5 


2-70 


301 


•7669 


•2378 


2-1855 


206-8 


•0105 


163 


» 5 


„ 4 


301 


3-32 


•8515 


•2640 


2-4495 


237-1 


0103 


182 


„ 4 


„ 3 


3-32- 


364 


•9047 


•2895 


2-7390 


272-4 


0100 


203 


„ 3 


„ 2 


3 64 


3-97 


•960 


•3168 


3-0558J 


313-7 


•0097 +. 


228 


„ 2 


„ 1 


3-97 


432 


•986 


•3451 


3-4009 + 


362-5 


•0093 + 


256 


„ 1 


>, 


4-32 


4-71 


•965 


•3764 


3-7773 + 


4200 


•0090+ 


288 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


(8) 


(9) 


(10) 


i 


* Fr 


"im flip "Po 


rmnln O' 


1343 x X ~ X ' 








! 




Jill \. ll\-j J. \J 


A 111 I 1 1 it \J 


log y - los 


\y 






t 

1 


From curve ; the 


rest fron 


1 equatioi 


1. + Mor 


3 or less 1 


mcertain. 


p 



THE LAWS OF CONDUCTION OF HEAT IN BAES. 



103 



TABLE X. — CASE II. 1|-inch Iron Bar, covered with Paper. Calculation of Area 
of Statical Curve of Cooling (F), and of the Conductivity at different 
Temperatures. 



Limits of Abscissae. 


Limits of Ordinates. 


M* 


Area 
M {y'-y). 


Total 

Area 

F. 


dv 
dx 


Con- 
ductivity, 
F. 
dv 
dx 


Corre- 
sponding 

Actual 

Temp. 

Cent. 
(H-13). 


X 


x' 


y 


y' 


Ft. In. 


Ft. In. 


















00 


IV. „ 


o- 


•021 


•980 


•0206 


... 








IV. „ 


III. „ 


•021 


•070 


•8305 


•0407 


•0613 


4-47 f 


01372 


17 


III. „ 


II. „ 


•070 


•282 


•7177 


•1521 


•2134 


16-3 


•01310 


26 


II. „ 


1.6 


•282 


•58 


•6935 


•2066 


•4200 


32-5 


•01292 


37 


I. 6 


I„ 


•58 


1-28 


•6317 


•4422 


•8622 


69-9 


•01234 


62 


I. „ 


„ 9 


1-28 


1-98 


•5728 


•4020 


1-2642 


1090 


•01160 


84 


„ 9 


„ 7-5 


1-98 


2-48 


•5551 


•2776 


1-5418 


137-6 


•01120 


99 


„ 7-5 


,. 6 


2-48 


3-14 


•5301 


•3499 


1-8917 


175-2 


•01080 


119 


„ 6 


„ 5 


314 


373 


•4840 


•2855 


2-1772 


206-5 


•01054 


134 


„ 5 


„ 4 


3-73 


4-41 


•4978 


•3385 


2-5157 


245 


•01027 


153 


„ 4 


„ 3 


4-41 


5-20 


•5055 


•3993 


2-9150 


292 


•00998 


176 


„ 3 


„ 2 


5-20 


605 


•5500 


•4675 


33825 + 


351 


•00964+ 


202 


„ 2 


„ 1 


6-05 


7-06 


•5401 


•5455 


3-9280+ 


423 


•00929 + 


234 


„ 1 


„ o 


706 


8-30 


•5147 


•6383 


4-5663+ 


512 


•00892+ 


273 


0) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


(8) 


(9) 


(10) 


* M = ( 


V4343 


x — x' 








% More 


or less uncertain. 




lo| 


yy'-\og 


y 


f Thei 


values of 


dv . 
-r— are al 
dx 


I from eqi 


lations, ai 


id theyal 


1 agree satisfactorily with projection. 



TABLE XL — CASE III. 1-inch Iron Bar, Naked. Calculation of Area of Statical 
Curve of Cooling (F), and of the Conductivity at Different Temperatures. 



















Con- 














Area 
M {y'-y). 


Total 


dv 


ductivity, 


Actual 


X 


x' 


y 


y' 


M 


Area 
F. 


dx 


F. 
dv 


Temp. 
Cent. 


















~ dx 


o+ii); 


Ft. In. 


Ft. In. 


o 
















OO 


IV. „ 


0- 


00185 


•820 


•0152 








o 


IV. ,, 


III. „ 


•0185 


•070 


•7515 


•0387 


0539 


5-52 


•00977 


16 


III. „ 


II. „ 


•070 


•258 


•7667 


•1441 


■1980 


1964 


•01008 


27 


II. „ 


I. 6 


•258 


•55 


•6605 


•1928 


•3908 


38-0 


•01029 


41 


I. 6 


I. „ 


•55 


1-185 


•6515- 


•4137 


•8045 


81-6 


•00986 


68 


I-„ 


„ 9 


1-185 


1-85 


•5612 


•3733 


1-1778 


124-1 


•00949 


94 


„ 9 


„ 7-5 


1-85 


2-33 


•5419 


•2600 


1-4378 


154-6 


•00930 


111 


„ 7-5 


„ 6 


2-33 


2-93 


•5456 


•3274 


1-7652 


193-6 


•00912 


132 


„ 6 


„ 5 


2-93 


3-44 


•5192 


•2648 


2-0300 


226-0 


•00898 


149 


„ 5 


„ 4 


3-44 


400 


•5526 


•3094 


2-3394 


264-4 


•00885 


170 


„ 4 


„ 3 


400 


4-54 


•6580 


•3553 


26947 


310-5 


•00868 


193 


„ 3 


„ 2 


4-54 


5 19 


•6229 


•4048 


30995* 


366 


*-00847 


221 


2 


., 1 


5-19 


5-92 


•6339 


•4627 


3-5622* 


432 


*-00824 


254 


„ 1 


„ o 


5-92 


6-75 


•6349 


•5270 


4-0892* 


512 


*'00799 


293 


! (i) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


(8) 


(9) 


(10) 








* | 


4ore or le 


ss uncert 


ain. 









104 PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 

110. Uncertainty, I have already said, attends the determinations of con- 
ductivity for the higher as well as those at the lowest temperatures. In fact, the 
former are (as will have been seen from the details already given) the results of 
analogies rather than of direct experiments. The experiments, whether Statical 
or Dynamical, rarely extended beyond a temperature of 200°, or at most 220° 
Cent. The results have been here carried out by the analogies afforded by the 
equations to the curves to nearly 300°. Nevertheless, the continuity of the law 
of conductivity diminishing with temperature, is consistently brought out by these 
approximations. 

111. In the preceding Tables the conductivity is expressed in terms of the 
amount of heat as unity, which is required to raise the temperature of one cubic 
foot of iron, by one degree Cent. It expresses the amount of heat reckoned 
in such units which would traverse in one minute across an area of one square 
foot, a plate of iron one foot thick, with the two surfaces maintained at tem- 
peratures differing by 1° Cent. 

112. If we now project the values of the conductivity of iron found in the last 
column but one of the three preceding Tables in terms of the thermometric tem- 
peratures (Centigrade) in the last columns, Ave are enabled to trace easily the 
connected results of the whole inquity. (See Plate V. fig. 4.) 

113. We tind that in each case the conductivity diminishes as the temperature 
increases; and that, for the next part, in a progressive manner. The variation 
with temperature is clearly most rapid at the low r er temperatures. 

114. The two first series agree very closely in their numerical results, with 
the exception of certain irregularities in the part of the curve where the tempera- 
tures are lowest ; which have already been in part accounted for (Arts. 55, 65, 
109). These two series belong to one and the same bar, though cooling under 
very different circumstances, owing to the largely increased radiating power 
conferred upon it by coating it with paper. And the value of the striking 
coincidence in the numerical results in Tables I. and II. is enhanced by the 
consideration, that the numbers expressing the conductivity are obtained bv 
taking the ratios of two different columns (7 and 8), which in the two Tables 
differ most widely, and the result cannot be even guessed at until the ratio is 
actually taken. 

115. The third series (Table X.) leads to numbers very sensibly differing from 
the two first series, yet following the same general law, the conductivity decreas- 
ing with temperature (excepting at the lowest part of the scale, where we find an 
anomaly corresponding to that noted in an early part of this paper (Art. 65), 
showing that the lowest portion of the statical curve has not in this instance 
been satisfactorily determined). The conductivity in Table X. is smaller 
throughout than in the tw r o former cases. It is believed that this can be 
satisfactorily accounted for by the different quality of the iron of which this 



THE LAWS OF CONDUCTION OF HEAT IN BAES. 



105 



bar was made, which came from a different manufactory, and was probably 
inferior in quality.* 

116. Tracing an interpolating curve through the projected observations of 
Cases I. and II., which run nearly parallel and at no great distance, at tem- 
peratures superior to 40° and do not diverge even in the higher and more 
hypothetical part of the diagram, and doing the same separately for Case III., we 

obtain the following numbers, purely as results of observation:— In the first 

F 

column of each division of Table XII., we have the ratio _ dv, which expresses 

dx 
the conductivity in terms of the heat required to raise a cubic foot of iron by 
one degree Centigrade. In the two following columns, we have the same reduced 
to the usual standard of conductivity in French and English measures re- 
spectively.f 

TABLE. XII. 



Temp. 


Cases I. and II. 


Case III. 




CONDUCTIVITY. 




CONDUCTIVITY. 


Cent. 


F 






F 
















"• = dv 


Units : Foot, 


Units : Centi- 


k = dv 


Units : Foot, 


Units : Centi- 




~ dx 


Minute and 


metre, Minute, 


~ dx 


Minute, 


metre, Minute, 






Cent. Deg. 


Cent. Deg. 




Cent. Deg. 


Cent. Deg. 





•01506 


•01337 


12-42 


•01117 


•00992 


• 9-21 


25 


•01391 


•01235 


11-48 


•01062 


•00943 


8-79 


50 


•01288 


•01144 


10-63 


•01014 


•00904 


8-37 


75 


•01205 


•01070 


9-94 


•00974 


•00865 


804 


100 


•01140 


•01012 


940 


•00940 


•00835 


7-76 


125 


•01088 


•00966 


898 


•00916 


•00813 


756 


150 


•01052 


•00934 


8-68 


•00895 


•00795 


7-38 


175 


•01018 


•00904 


8-39 


•00877 


•00779 


7-23 


200 


•00987 


00876 


814 


•00860 


•00764 


7-10 


225 


•00958 


•00851 


7-90 


•00844 


•00749 


696 


250 


•00930 


•00826 


767 


•00826 


•00736 


6-84 


275 


•00902 


•00801 


7-44 


00815 


•00724 


6-72 



117. The coincidence of the results in the second column with the results of 
the provisional reduction in the case of the 1^-inch bar, made in 1852, and 
printed at Art. 33, page 144, of the former part of this paper, is both striking 
and satisfactory. For it shows, as I there anticipated (Art. 38), that the 
method is, to a great extent, independent of the ordinary instrumental errors, 

* Dr Matthiesson in his Experiments on the Electric Conductivity of Iron (Phil. Trans., 1863), 
has found nearly equally wide variations in different specimens. 

f If the numbers in the first column of each division of the Table be called A, then A x 888 
will express the conductivity in water-measure for the foot, minute, and Cent, degree ; and A x 825 
gives the numbers in the third column, where the centimetre is substituted for the foot. 

VOL. XXIV. PART I. 2 F 



106 PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 

and even of the laborious computations which have formed the basis of the pre- 
sent paper. 

118. In the preceding Table I have completed the series for lower temperatures, 
where the observations were less accordant, in the following way : — I have 
assumed that the most trustworthy part of the observational curves are those 
between the actual temperatures of 40° or 50 s and 150° or 160°, and that within 
moderate limits, the conductivities {k) may be represented in terms of the tem- 
perature (t), by such a formula as 

h = A + at + hi 2 

In the case of the l^-inch bar, I find for these constants 

A = -01506 a = - -0000488 b = + -000000122 

From which the conductivities corresponding to and 25° have been interpolated. 
In the case of the 1-inch bar the constants are — 

A -01117 a=- -0000235 &=+ -000000058. 

119. I must here observe, however, that the above form of relation between 
k and t, which has been applied by Dr Matthiessen, in his extensive and im- 
portant researches on electric conductivity, does not satisfy the form of our con- 
ductive curves, Plate V. fig. 4, except through a limited range. I have reason, 
however, to think, that down to 0° of temperature it may be sufficiently exact. 
The " percentage decrement" of the conductivity between 0° and 100° is 24-5 
for the larger bar of iron, and 159 for the smaller one. As in the case of Dr 
Matthiessen's electrical experiments, the " percentage decrement" diminishes 
with the conducting power, and in almost exactly the same proportion.* The 
numerical values in either case are, however, considerably smaller for heat than 
those obtained by Dr Matthiessen for electricity. 

120. With this exception, however, there is an agreement in the character of 
the metals (so far as is yet known) in conducting heat and electricity. (See Art. 2 
of this paper.) 

§ VII. — Concluding Bernards and Suggestions. 

121. In Art. (15) of the first part of this paper, I expressed my desire to afford 
to future experimenters every aid I possibly could to resume and extend my obser- 
vations (confined, unfortunately, to only one metal — iron), and to furnish them 
with such advantages as my experience afforded, as well in methods of observa- 
tion as of reduction. 

122. It was especially with this view that I have spent what may perhaps 
appear an undue amount of labour on the reduction of the experiments considered 

* Phil. Trans. 1863, p. 380. 



THE LAWS OF CONDUCTION OF HEAT IN BARS. . 107 

in the present paper. I do not, however, regard this labour as wasted, for the 
knowledge thus acquired of the nature of the remarkable curves of which it treats 
will enable a future observer to attack the question in a far more direct manner, 
and to obtain, with comparatively little trouble, numerical determinations of the 
conductivity of the metals under ordinary circumstances, and adapted to most 
purposes of theory or practice, 

123. Suggestions as to Experiments. — After mature consideration, I do not 
think that the experimental methods require almost any modification. The 
independence of the results of any moderate error in the thermometers seems 
satisfactorily proved (Arts. 38 and 117) ; and if the object be merely to ascertain 
the conductivity and " percentage decrement" for a number of metals, it may 
easily be done without pushing the observations to the high temperatures used 
in my experiments, which are always a fertile source of difficulty and error. If, 
for instance, an extreme temperature of 120° or 140° Cent, only was aimed at, 
shorter bars might be used ; the heat would be more manageable and more 
quickly attained ; the thermometers would be more easily made, more easily 
used, and subject to far smaller corrections ; and the dynamical experiments 
especially, would be freed from an anxious and troublesome source of error, 
arising from the irregularity of the primitive distribution of the heat in the cooling 
bar (Arts. 25, 26, and 90). 

124. A more exact knowledge of the form of the statical curve of temperature 
in any case may be obtained by using sources of heat of progressively lower tem- 
perature, as explained in Arts. 27 and 58. 

125. It is probable that very good results might be obtained by simply using 
boiling water as a source of heat at the hottest end of the bar, than which nothing 
can be more manageable. The duration of the statical experiments could thus 
be much reduced, and the temperature of the air of the apartment rendered more 
stable. The difficulties referred to in Arts. 65, 109, as to the determination of 
very small excesses of temperature next the cool end of the bar might thus be 
in a great measure removed. Indeed, it would be a worthy object of study, in a 
theoretical point of view, to determine the form of the Statical and Dynamical 
curves for those low temperatures more accurately than I have done. I cannot 
but suspect an anomaly in the conduction of heat when the temperature varies 
with extreme slowness from point to point, which my observations rather indicate 
than establish* 

126. Another experimental point of interest for the theory would be to estab- 

* I may be allowed to state here generally, that this anomaly would apparently assign a too 
great conducting power to iron at low temperatures than we can readily admit. [The case of the 
1-inch bar might rather lead to an opposite conclusion, but I have less confidence in the observa- 
tions made on it for very small excesses of temperature ] Both the statical curve and the curve of 
cooling deviate more and more from the logarithmic form as the temperature-excesses diminish. 



108 PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 

lish, for a few points of a metallic bar, the difference between the superficial 
and the internal temperature of the bar in any transverse section. This might 
be done by thermo-electric methods, such as, I think, were used by the late M. 
Langberg of Christiania in his experiments on the conduction of heat in bars. I 
made some attempts (which were not unpromising) in a different way, by applying 
to the surface of the bar small portions of fusible alloys or other substances, lique- 
fying at definite temperatures. There did not appear to be much difficulty by 
gently sliding these proof-pieces along the bar from the cooler towards the hotter 
part, of ascertaining with considerable precision the co-ordinate of the superficial 
point, corresponding to the fusing temperature of the alloy or other substance used. 
The five following substances, in a descending scale, were found to have tolerably 
definite fusing-points, and to be sufficiently suitable for the experiment :— Tin ; 
solder (tin 9 parts, lead 5 by weight) ; fusible metal (consisting of bismuth 2 
parts, lead 1 part, and tin 1 part by weight) ; napthalic acid ; and bees-wax. The 
fusing temperatures of the three first were carefully ascertained by direct experi- 
ment to be — 

Tin,* . 229°0 Cent. = 444°-2 Falir. 
Solder, . 181°-6 „ =358° 9 .. 
Fusible metal, 94M5 „ =20l°4 

The fusing points of the others were not ascertained by me. 

127. The experiments which I made in this manner were entirely tentative 
and preliminary. The following is a specimen: — Statical experiment; 1851, 
March 14. l|-inch bar, naked [see Table I., page 78 of this paper.] " At l h 40 m 
I tried the following experiment to test the difference of temperature of interior 
and exterior of bar. Taking small sharp-pointed pieces of tin [and] fusible 
metal (prepared on purpose, bismuth 2, lead 1, tin 1 by weight), I rubbed them 
gently on the surface of the iron bar till I found the melting point, keeping 
them gently in motion so as not to allow the surface to heat beneath them. I 
fixed these points with very considerable exactness, in the case of the fusible 
metal (the best observation), to perhaps within ^th inch. I did not find the 
position sensibly [to] vary on the centre of the top, and on the centre of the side 
of the bar, nor even towards the angle of the bar (with the fusible metal). These 
experiments deserve repetition. 

" l h 40 ra Tin melted when rubbed on ) 

the centre of one side of the bar, j> from origin at the edge of the crucible, 
at . . ft. 065 in. ) 

Fusible metal, . . 10-45 „ ,, „ „ „ 

Bees- wax, . . 1 4 7 „ „ „ 

* The melting point of tin seems to be 'one of the best determined of the higher temperatures. 
According to Crichton, Senior (of Glasgow), it is 442° Fahr. [T. Thomson]; Kupffer, 446°; 
Daniell, 441°. On the melting point of lead, see Art. 70. 



THE LAWS OF CONDUCTION OF HEAT IN BARS. 109 

128. Suggestions as to Reductions. — Were any one desirous of pursuing the 
subject of the theory of conduction into its details, I should be disposed to 
recommend the employment of Biot's formula of 5 constants (used to express 
the elasticity of steam), instead of Roche's, containing 3 constants, which we 
have here used, see Art. QQ. The method of calculation (which is necessarily 
laborious), is given in Regnault's large treatise on the Theory of the Steam 
Engine* For any merely practical purpose, however, this is not required. An 
experimenter desiring to compare the conductivity and " percentage decrement" 
of different metals, may reasonably confine his attention between the useful 
limits of 20° and 120°, or at most 140° Centigrade. For that interval, Roche's 
formula will suffice. And the chief use of the formula is to obtain readily and 

accurately the differential co-efficient j- (see Arts, 71 and 78), on the determina- 
tion of which the value of the conductivity mainly depends. 

129. Though I would not recommend the attempt to proceed by graphical 
methods alone, they are an invaluable help, and also serve as a check to the 
calculations. Where these are not made throughout in duplicate, the use of 
curves ensures the detection of any material error of the computer. The check 
by taking first and second differences should also not be disregarded. The curves 
of cooling may be treated in a similar way. 

130. I believe, however, that very fair results might be rapidly and approxi- 
mately obtained by graphical methods alone. The curves of Statical Temperature 
and of Cooling being first projected in the usual way, tangents might be drawn 
mechanically for ordinates successively differing by 10°. The ordinate divided 

by the subtangent found would give the numerical values of -r- and j They 

would no doubt be somewhat irregular from the clumsiness of the graphical 
process; but being projected in terms of x and v respectively, and equalizing 
curves drawn through them, fair results would be obtained-! The " statical curve 
of cooling" is then constructed without any calculation whatever ; and for evalu- 
ating its area up to any limiting ordinate, it might be sufficient that the curvilinear 
space it encloses should be defined on writing paper and cut out with scissors : 
the successive portions being weighed, would represent the flux of heat in known 

* I ought perhaps to mention the formula which Professor Rankine has applied with success 
to express the elasticity of steam at all temperatures (Edin. Phil. Journ. 1849, vol. xlvii. p. 28, and 
Philos. Mag. 1854, vol. viii. p. 530). It is as follows: — 

log P = A - -- % 
r r 

where P is the elasticity of vapour, and r the temperature reckoned from an absolute zero ( — 274° 
cent). In applying the formula to the temperature of a bar, there can be no natural zero from 
which the lengths are reckoned along the bar; and therefore the constants, instead of three in 
number, may be reckoned as four ; putting v instead of P in the above formula, and, instead of r. 
writing a; + D, D being some fourth constant. (See article 67.) 
f This method was used by me in 1852. 

VOL. XXIV. PART I. 2 G 



HO INQUIRY INTO THE LAWS OF CONDUCTION OF HEAT IN BARS. 

units. I have little doubt that the results would come out within one or two 
hundredths of those obtained by elaborate calculations. 

131. I have only to add, that the greater part of the computations in this 
paper were executed by Mr Alexander Pirie of St Andrews. Every part of 
the projections and graphical interpolations was performed by my own hand ; 
and my thanks are especially due to the Messrs Johnston for the unusual care 
with which they have been reduced in scale, and transferred to copper, as seen 
in the Plates. 

St Andrews, April 1865. 



( 111 ) 



IX. — Some Observations on the Cuticle in relation to Evaporation. By John 
Davy, M.D., F.R.S. London and Edinburgh. 

(Read 1st May 1865.) 

Though it is generally admitted that the cuticle performs an important part 
in retarding and regulating evaporation from the surface of the body, yet I am 
not aware of any inquiry hitherto made to determine the fact with exactness. 

On account of the importance of the subject, I have been induced to engage 
in it. The experiments instituted for the purpose have all been of a very simple 
kind and easily made. They were on the similar parts of dead animals, detached 
immediately or very soon after the animals had been killed. From one speci- 
men in each instance, the cuticle with the cutis, or the cuticle alone, was removed ; 
whilst from the other these parts of the integuments were left entire. Each was 
carefully weighed, and then suspended, exposed to the air, side by side. Day 
after day, with occasional interruptions, or hour after hour, the weighing was 
repeated, and the result in the loss sustained was noted down. The experiments 
were made, when not otherwise mentioned, as just described, in a room in which, 
except in the height of summer, there was commonly a fire by day, its tem- 
perature during the day and night varying from about 50° of Fahr. to 55° and 58°. 
The animals affording the subjects of the trials were the trout, frog, toad, hare, 
rabbit, pig, thrush, common fowl, blue tit. Even at the risk of tediousness, I 
shall give the results of the weighing in some detail, — exactness in such trials 
being the first thing necessary. 

1. The Common Trout (Salmo fario). Two trouts were selected of the same 
size. From one (No. 1) the greater part of the skin was removed, when it weighed 
112 grs. The skin of the other (No. 2) was left on entire; it weighed 267 grs. 
This was on the 20th October. 

October 21. No. 1 hacl lost 32-0 grs., or 28-5 per cent. 



>5 


j> 


2 


;> 


31-7 


?> 


19-0 


22. 


!) 


1 


)) 


55-3 


j» 


50-6 


5J 


J) 


2 


)) 


66-0 


51 


390 


24. 


>) 


1 


'J 


80-0 


!> 


71-4 


)) 


)> 


2 


)) 


108 


)) 


64-6 


27- 


3) 


1 


>) 


828 


)5 


74-0 


)J 


!> 


2 


)) 


120-8 


!] 


72-0 


28. 


;> 


1 


5) 


83-0 


It 


74-2 


J) 


5> 


2 


>! 


1213 


>•> 


72-6 


30. 


>5 


1 
2 


') 


831 

121-8 




74-28 
72-90 



VOL. XXIV. PART I. 2 H 



112 dr davy's observations on the cuticle 

Weighed again on the 31st, there was no further loss. Both were dry and rigid, 
and free from any unpleasant smell. 

Another trial was made in the following manner : — a trout, just after it had 
been taken, October 26th, was divided in the line of the spine. From one 
moiety (No. 1) the skin was removed, when it weighed 1177 grs. On the other 
(No. 2) the skin was left; it weighed 837 grs. The head had previously been 
detached and the fish eviscerated. 

October 27. No. 1 had lost 59-7 grs., or 507 per cent. 

„ „ 2 „ 43-2 „ 50-4 „ 
28. „ 1 „ 88-7 „ 75-3 „ 

„ „ 2 „ 632 „ 75-5 „ 
30. „ 1 „ 90-0 „ 76-4 „ 

„ „ 2 . „ 636 „ 75-9 ,, 



On the following day the weight of No. 2 was the same, that of No. 1 was ■ 1 gr. 
less ; both were dry and rigid. 

2. The Frog {Rana temporaria). A female on the 7th April was killed by 
decapitation. After the application of a ligature to each thigh, just at the junction 
with the pelvis, they were detached. From one (No. 1) the integuments were 
removed; it weighed 559 grs. On the other (No. 2) they were left; it weighed 
69 9 grs. 

April 8. No. 1 had lost 17'2 grs., or 307 per cent. 

„ „ „ 2 „ 204 „ 29-2 „ 

„ 9. „ 1 „ 34-6 „ 61-9 „ 

„ „ „ 2 „ 47-3 „ 60-5 „ 

„ 10. „ 1 „ 39-0 „ 700 „ 

„ „ „ 2 „ 48-2 „ 690 „ 

» 11. ., 1 » 39-5 „ 70-6 „ 

„ „ „ 2 „ 49-6 „ 70-9 „ 

., 12. „ 1 „ 39-7 „ 71-0 „ 

„ „ „ 2 „ 50-0 „ 715 „ 

„ 13. „ 1 „ 400 „ 71-4 „ 

„ „ » 2 „ 50-2 „ 718 „ 

After this they sustained no further loss ; on the contrary, the air being damper 
they gained slightly in weight. In the dry and rigid state to which they were 
reduced they were put into water. Taken out after three hours and wiped to 
remove adhering water, No. 1 had gained 10*8 grs., No. 2, 148 grs. Immersed 
again and left in twenty-four hours, each had recovered its original weight. 

3. The Toad (Bufo vulgaris). A similar trial was made with the lower ex- 
tremities of a large toad, killed on the 11th July, when in full vigour. The 
extremity (No. 1), deprived of its integuments, weighed 80 grs. ; the other, with 
the integuments on (No. 2), 82'3 grs. 



IN RELATION TO EVAPORATION. 



113 



July 12. No. 1 had lost 39-0 grs., or 487 per cent. 



„ „ 2 


>J 


37-60 „ 45-5 


13. „ 1 


)> 


51-90 , 


64-9 


„ „ 2 


>> 


54-00 „ 65-2 


17. „ 1 


f) 


53-07 , 


663 


„ ., 2 


»i 


56-85 , 


, 69-0 



Neither sustained any further loss from exposure. The thermometer during the 
time ranged from 65° to 68°. 

4. The Rabbit (Lepus cuniculus). From a wild one recently killed the skin was 
removed from the under surface of one ear and left on the upper ; it (No. 1) 
weighed 34'5 grs. Of the other (No. 2) the skin was left on both surfaces ; this 
weighed 43 1 grs. They were placed on a stove, side by side, the under surface 
of each uppermost ; a thermometer close to them was 93°. 

In 1 hour 35 minutes No. 1 had lost 15-5 grs., or 44-9 per cent. It has become rigid. 



It is rigid only at its edge. 



„ 3 


, 35 


„ 10 


, 35 


„ 24 „ 

„ „ „ o 



2 


34 „ 7'8 


1 , 


19-1 


, 55-2 


2 , 


6-0 


, 13-9 


1 , 


20-9 


, 60-5 


2 , 


8-5 


, 19-7 


1 


22-3 , 


, 64-6 


2 , 


16-2 , 


, 37-6 



No. 1 sustained no further loss ; No. 2 continued to lose weight, gradually dimi- 
nishing in flexibility up to 289 hours, when it had lost 28*1 grs., or 65 - 2 per cent., 
and had become hard and rigid. 

5. The Hare (L. timidus). On the 5th November, from a hare recently killed, 
one ear (No. 1) was immersed in boiling water for a minute, after which, when 
cold, the integument was easily removed, this from the outer surface only ; it 
weighed 81*8 grs. On the other ear (No. 2) the integuments were left entire; 
it weighed 1097 grs. They were placed on paper on a stove, when the tempera- 
ture was about 100°. 

In 20 hours No. 1 had lost 57 grs., or 69-6 per cent. It had become shrivelled and hard. 

>> 

„ It sustained no further loss. 

„ Is still tolerably soft and supple. 

„ Suppleness much impaired. 

„ It is now hard and little flexible. 

It should be mentioned that it was only by day that the temperature was kept 
up to about 100°. 

6. The Pig (Sus vulgaris). As soon as killed, March 24th, a ligature was 
applied to one ear, and the portion included cut off; it (No. 1) weighed 1285 grs. 
From the other ear a portion similarly included (No. 2) was cut off ; after the 
application of boiling water and the removal of the cuticle, it weighed 159 grs. 
They were suspended fully exposed to the air. 



)) >> 


» 2 


7-7 


>? 


7-0 


24 „ 


„ 1 


57-8 


>) 


70-6 


)» )> 


„ 2 


37-5 


)> 


34-2 


48 „ 


„ 2 


47-7 


)3 


43 5 


72 „ 


„ 2 


58-9 


}> 


53-7 


96 „ 


„ 2 ; 


61-5 


>> 


56- 


192 „ 


„ 2 


67-6 


}> 


61-6 



114 



DR DAVY'S OBSERVATIONS ON THE CUTICLE 



March 30. No, 


, 1 had lost 


81 


grs., 


or 6-6 


per cent. 




>> n o 


2 


5) 


56-0 


jj 


36-6 


)> 




5) 31. ,, 


1 


» 


181 


j) 


140 


>> 




)> » J) 


2 


» 


107-0 


>) 


67-2 


>> 


It is shrunk and rigid. 


April 3. „ 


1 


>> 


360 


?) 


28-1 


i) 




>» )> >> 


2 


)» 


114-3 


»> 


71-7 


15 


It sustained no further loss. 


)> 9. ,, 


1 


)> 


61-0 


>; 


47-4 


)) 


Its softness and suppleness diminishing. 


„ 12. „ 


1 


)) 


71-6 


5) 


55-6 


)) 


Is now rigid. 



7. The Barn-door Fowl (Gallus domesticus). As soon as killed, the wattles of a 
cock two years old were cut off, a ligature having been previously applied at the 
base of each. One (No. 1), from which the cuticle was scraped off, weighed 62*2 
grs. ; the other (No. 2), on which the cuticle was left, weighed 79 5 grs. 



October 21. No. 1 has lost 25*3 grs., or 40 6 per cent. 



?) 


>j 


2 


22. 


)> 


1 


5) 


»> 


2 


24. 


5> 


1 


>> 


>) 


2 


27. 


5> 


1 


)> 


>' 


2 


30. 


)) 


1 
2 



14-8 


, 186 


356 


., 57 2 


26-4 


33-2 


41-7 , 


„ 67-0 


42-5 , 


, 53-4 


447 , 


, 71-8 


52-8 


66-4 


45-2 , 


, 72-3 


55-6 „ 


700 



It is hard and rigid. 



{Excepting margin, still retains some 
flexibility. 



Is quite rigid. 



8. The trial was repeated on the legs of a fowl on the 18th May, when the 
temperature of the room was 65~, without a fire. They were separated at both 
their j unctions, viz., femur and tarsus. One (No. 1), stripped of its integuments, 
weighed 835 5 grs. ; the other (No. 2) its integuments on, the skin drawn over 
each stump and secured by a ligature, weighed 889 grs. This without the 
feathers, which had been removed. 



May 19. I! 


fo. 1 has 


lost 115-5 


grs-, 


or 13-8 


>> >) 


„ 2 


8-5 




„ 


■9 


„ 20. 


„ 1 


201-5 




), 


24-0 


J) J? 


„ 2 


145 




>> 


16 


„ 21. 


i— i 


2660 




)> 


31-8 


5) )> 


„ 2 , 


20-0 




7> 


2-2 


„ 22. , 


, 1 , 


3200 




!, 


38-3 


■>j >? "> 


, 2 , 


25-5 




?> 


2-8 


rune 5. , 


, 1 , 


81-5 




JJ 


100 


)t )? ? 


, 2 


487-0 




3; 


58-0 


„ 17. , 


, 2 , 


522- 




j) 


62-4 



, Is free from any unpleasant smell. 

, Is becoming putrid. 

i Not again weighed, owing to its putrid state. 

No further loss. 

Comparing the results of the one covered with integument with those of the 
other deprived of it, apart from the vastly greater loss of water by evaporation, 
the other changes were strikingly contrasted. No. 1, that deprived of integu- 
ment, excepting its loss of water and its hard, rigid state in consequence, seemed 
little altered ; when moistened it was quite free from any putrid taint, and its 
muscles exhibited their striated structure with undiminished distinctness. No. 2, 
on the contrary, that on which the integument was left — that still retaining its 



IN RELATION TO EVAPORATION. 



115 



toughness and little changed — was found, when an incision was made into the 
contained muscles, to be undergoing the putrefactive change, denoted by the 
sickening, putrid smell, the softening of fibre and the loss of striated structure, 
with the appearance of many crystals, chiefly four-sided prisms, which were pretty 
readily dissolved in dilute acetic acid. 

9. The Martin (Hirundo urbica). A young bird, fledged, on the 14th July, 
was found dead, thrown out of its nest by the female bird, which had been for- 
saken by her mate, probably killed. The nestling weighed 230 grs. One of its 
thighs (No. 1), stripped of integuments, weighed 3-6 grs. ; the other limb (No. 2), 
the entire lower extremity with integuments on, weighed 7*6 grs. 



July 15. No. 1 had lost 2-3 grs 



16. 
19. 
22. 

25. 



1-4 

2-3 
36 
3-9 

4-0 



or 63-8 per cent. 
184 „ 
30-2 „ 
47-3 „ 
61-3 „ 

52-6 



It had no further loss. 



It sustained no further loss ; proportionally 
it was so much less than that of No. 1, 
from having less muscle, more bone, &c. 



10. The Thrush (Turdus musicus). A male was shot on the 15th July. 
Its leg, deprived of its integuments (No. 1), weighed 32*2 grs. ; the other leg, 
with foot, the integuments left on, but without the feathers (No. 2), weighed 
42-1 grs. 



July 16. 


No. 


1 had lost 13-2 


grs 


, or 41*0 per cent. 




» !> 


JJ 


2 


Jj 


2-8 




6-8 „ 




„ 17. 


JJ 


1 


Jj 


19-2 




, 59-6 „ 




jj >' 


jj 


2 


}> 


46 




10-9 




„ 19. 


JJ 


1 


JJ 


20-7 




, 64-2 „ 




J J >> 


;j 


2 


jj 


12-6 




30-0 




„ 27. 




1 


jj 


21-0 




65-1 


No further loss 



It was rigid, and the muscles were well preserved ; perfectly free from putrid 
taint. No. 2 was not weighed after the 19th ; then examined, it was found 
full of magots of the flesh-fly, twenty-seven in number, all of about the same size, 
about *4 inch in length ; their weight was 16'6 grs. The muscles of the leg 
were entirely devoured ; what remained, namely, skin and bone, weighed 12-9 
grs. The larvse were partially distended with putrid matter of muscle, in a semi- 
fluid state, of a reddish hue, and like chyme in appearance. As seen under the 
microscope, it was found to consist of extremely minute granules, amongst which 
were dispersed oil globules of different sizes, and some crystals, mostly prismatic. 
In these larvae we have a striking example, it may be remarked, of highly 
organised beings, structurally consisting of striped and unstriped muscles, of 
trachea?, of nerves and various glands, &c, formed in so short a time by assimi- 
lation of dead putrid matter. 

11. Of another thrush, killed on the 27th July, one thigh and leg (No. 1), de- 
prived of integuments, weighed 50*1 grs.; the other leg and foot, stripped of 

VOL. XXIV. PART I. 2 I 



116 DR DAVY'S OBSERVATIONS ON THE CUTICLE 

feathers, and without the thigh (No. 2), weighed 426. The integuments were 
left on, and to prevent access to the muscles and the deposition of the ova of the 
flesh-fly, sufficient skin from the thigh was drawn over the stump and secured 
from ingress by a ligature of fine silk. 

July 28. No. 1 had lost 22-2 grs., or 44-3 per cent. 

„ „ „ 2 „ 2-7 „ 60 „ 

„ 29. „ 1 „ 31-6 „ 63-0 „ 

„ » „ 2 „ 45 „ 100 „ 

„ 31. „ I „ 334 „ 66-6 „ 

„ „ „ 2 „ 6-75 „ 158 „ 

Aug. 4. „ 1 „ 33-55 „ 66-9 „ No further loss. 

„ „ » 2 „ 14-6 „ 34-0 „ 

7. „ 2 „ 21-6 „ 50-0 „ 

„ 10. „ 2 „ 25-2 „ 591 „ 

In both instances, in the dried state to which they were reduced, little change 
had taken place. Even when examined now, after eight months, the muscles are 
found to retain their striated structure. In the instance of No. 2, this was pro- 
bably owing to the pretty rapid drying from the small bulk of the limb. 

12. I will mention one example more, a trial made in winter, between January 
the 4th and March the 14th, in a room the temperature of which seldom exceeded 
50°. The Blue Tit (Parus coeruleus) was the subject of the experiments. One. 
deprived of its skin (No. 1), weighed 169 grs. ; another (No. 2), deprived merely of 
its feathers, weighed 122-3 grs. Without giving the details of the weighing at short 
intervals, it may suffice to state that No. 1 had lost in twenty-six days 105 grs.. 
or 62 per cent. ; whilst No. 2 had lost 51 - 4 grs., or only 37 per cent. The first 
had become quite rigid and hard, and sustained no further loss ; the second con- 
tinued to lose weight, but so very slowly, that on the 14th March it was not 
thoroughly desiccated. It had lost 83*1 grs., or 60 per cent. 

Whilst the results which have been described sufficiently show the powerful 
influence of the integuments in moderating evaporation, if we compare those 
obtained in the experiments on different animals a marked difference is notable. 
The moderating or retentive power of the integuments of the frog and toad is 
seen to be lowest, that of the trout next, that of the mammalia higher, and that 
of birds highest. 

In the instance of the common fowl the thigh showed a much more retentive 
power than that of the wattle ; and it can hardly be doubted that were trials 
made of different parts of any other animal, a variety of moderating influences 
would be witnessed, according to the degree of thickness of the covering and 
difference of physical structure. 

As the cuticle is considered anorganic, may not the part it performs in rela- 
tion to the checking of evaporation in the living body be held to be much the 
same as in the dead body ? 



IN RELATION TO EVAPORATION. 117 

In the majority of the experiments described, the cutis was removed with the 
cuticle. . The results might appear more satisfactory if the cuticle alone had been 
abstracted — this a difficult matter, so difficult, that I rarely attempted it — but, 
inasmuch as the cutis does not seem to exercise any limiting power on evapora- 
tion, may it not be regarded as inoperative or impassive, and to have no material 
vitiating effect on the results ? 

Viewing the function of the cuticle physiologically, must it not be considered 
as intimately connected with animal heat ? Thus, where its retentive, moderat- 
ing power is lowest, as in the instance of the batrachians, is it not operative in 
preserving these comparatively cold-blooded animals cool ; and vice versa in the 
instances in which its power is highest, in birds, is it not conducive to the pre- 
servation of the elevated temperature for which they are remarkable ? 

A more important function, it may be inferred, is performed by it, associated 
with the preceding, namely, of preventing a too rapid loss of water from the 
system, and especially from the blood, thus preserving this vital fluid of a proper 
degree of dilution, and the solid parts of a proper degree of moisture and flexi- 
bility. In cases of extensive burns, when a large surface of integument has been 
destroyed, the loss of the aqueous portion of the blood is remarkable. In those 
cases which have been fatal, the blood has been found by M. Baraduc dark and 
inspissated, and the viscera surprisingly dry, with an absence of fluid in all the 
serous cavities. This inquirer, indeed, considers the gravity of burns in propor- 
tion to the amount of abstraction of fluid or the drying ; and accordingly in the 
treatment he holds it to be a principle to counteract this as much as possible by 
keeping the patients many hours in a bath daily, aided by the use of diluents, and 
by the dressing of the burnt parts with cerate. 

In the experiments on the limb of the fowl and of the thrush, as well as 
in all the others, the results show how much the rapid drying of the parts 
deprived of their integuments checks and prevents putrefaction at a certain tem- 
perature, and vice versa, how a retardation of drying, from the integuments being 
left on, favours putrefaction. And this it may be inferred, much in the same 
manner as an atmosphere loaded with moisture promotes the same change.* 

* A simple experiment illustrates this. Two portions of recently killed lamb were selected. 
One (No. 1) weighing 168-5 grs. was suspended by a thread, freely exposed to the air of a room 
varying in temperature from 60° to 65°, i.e., the day and night temperature. The other (No. 2), 
weighing 1601 grs., was suspended hanging free in a small glass receiver, in which was a little 
water, and was so covered as to allow ingress of air, and yet almost to prevent any evaporation. The 
results were strongly marked. No. 1 lost weight rapidly, and soon became hard and dry without 
acquiring any putrid taint. No. 2, on the contrary, softened and actually liquefied, at the same time 
becoming extremely putrid. In an experiment similarly conducted over water — but the water 
exhausted of air and in vacuo — the muscle escaped putridity. This, from the llth July to the 20th 
August, illustrating in addition, I may remark, the difference as regards tendency to putrefaction 
between muscle and blood ; the latter, as I have shown elsewhere (p. 25 of this volume), undergoing 
the putrid decomposition, even in vacuo, being impregnated with oxygen. 



118 DR DAVY'S OBSERVATIONS ON THE CUTICLE 

Why muscle deprived of its integuments should escape putrefaction, most 
other conditions favouring, is not very obvious to reason. Whether electricity is 
concerned in any way in the prevention is open to question. Be this as it may. 
the property is an important one, economically considered, and deserving, I can- 
not but think, of more attention than it has commonly received. The fact that 
meat, when cut into thin slices, can by drying be kept in a state fit for food even 
within the tropics, where putrefaction proceeds at so rapid a rate, is well known. 
The Boucaniers, we are informed, who, in the beginning of the last century, were 
such formidable pirates in the West Indies, depended very much for subsistence 
on meat thus prepared. Pere Labat, in his abridged history of St Domingo, 
describes this meat, calling it by its popular name, " Viandes boucannes," as 
excellent ; and he details the exact method of preparing it, as obtained from the 
wild hog, and from cattle run wild in the forests of that island.* Now, con- 
sidering the qualities of such meat, free from the defects of salted meat, the con- 
centrated nourishment it affords, and that of an agreeable kind, and easily 
cooked when softened by water, it seems peculiarly fitted for the army and navy 
in protracted campaigns and in long voyages, and also for the use of travellers 
in countries where subsistence is precarious. A method very similar to the pre- 
ceding, I am informed by Sir John Richardson, is employed by the North 
American Indians, in summer and autumn, for preserving the flesh of deer ; 
they, like the Boucaniers, bring in the aid of smoke, but chiefly for the purpose 
of protecting the meat from flies.-j- The dried meat powdered, mixed with lard 
or marrow, forms pemican, which has been of such inestimable value to arctic 
explorers.:]: The same Indians are well acquainted with the effect of skinning 
an animal in retarding its putrefaction. It is a practice of theirs to remove the 
skin with as little delay as possible, eviscerating their game at the same time. 

That thorough desiccation should have the effect of preserving meat from putre- 
factive change is obviously owing to an arrest of chemical action, the presence of 
a certain portion of water being essential to such action. § 

* Nouveau Voyage aux Isles de l'Amerique, &c. Par R. P. Labat. Tom. iii. p. 132. 

t When dry, even muscle no longer attracts the flesh-fly ; it is the moist putrefying flesh which 
allures it, that being alone suitable to the development of its ova. 

| A specimen of pemican (for which I was indebted to Sir John Richardson), about twelve 
months old, of the best quality, I found composed of — 

84 88 fat, 

11 77 muscular fibre chiefly, 
3 35 water. 
The fat consisted of oleine or elaine chiefly, and stearine. The muscular fibre, moistened, was found 
unaltered as to striated structure. 

§ In 1852 I put by, merely wrapped in paper, portions of pork, mutton, beef, fowl, common 
trout, pollack (Gadus pollachius). Tbey were left in the drawer of a table, in a room in which, 
during three-fourths of the year, there was a fire. Examined in December 1864; in all of them, 
with one exception, the muscular fibre exhibited the original striated structure distinctly. The 
exception was that of the trout, in the muscular fasciculi of which the striae were less distinct 
Pemican, which had been kept two years (a portion of that of which the composition is given in the 
preceding note), exhibited the striated muscle with perfect distinctness. 



IN RELATION TO EVAPORATION. 



119 



The same protection from change is witnessed, as is well known, in vegetables, 
from the removal of their aqueous portion. And in them, too, the cuticle 
appears to act a part in many instances similar to that of the animal cuticle in 
retarding evaporation. I may mention an instance or two in illustration, select- 
ing a tuber, the potato, and a fruit, the apple, these being striking examples : — 

On the 22d June, three potatoes of the kidney kind were taken from the 
ground : one (No. 1) had its skin left on — it weighed 295*2 grs. ; another (No. 2) 
had its outer skin removed — it weighed 181*7 grs. ; a third (No. 3) had its outer 
and very fine inner skin both entirely removed — it weighed 263*2 grs. They 
were placed on the chimney-piece, where the temperature throughout the year 
varied inconsiderably, ranging from about 50° to 60°. The three were weighed 
from time to time ; the loss per cent., as found on each weighing, is given in the 
following table : — 



June 


24. No 


1 lost 


7 8 per 


cent 


, No. 2, 46-5, 


No. 


3, 54-0 


u 


27. 


)> 


88 


39 


„ 66*4, 


ii 


70'2 


33 


30. 


>) 


104 


33 


„ 72-6, 


ii 


73-3 


July 


6. 


)? 


11-4 


33 


„ 74-9, 


33 


75-8 


n 


11. 


11 


12-6 


33 


„ 75-7, 


33 


77*8 


>> 


22. 


)> 


13-1 


3) 


„ 75*8, 


33 


78-6 


August 


5. 


j) 


13-9 


>> 


„ 75-9 ; 


33 


79-8* 


September 


10. 


93 


15-8 


)> 


No further loss 


33 


85*7f 


December 


1. 


53 


21 -0| 


I) 




33 


862 


February 


2. 


>» 


27*5§ 


3) 


No further loss 


March 


14. 


3> 


32-7II 


3> 









In these instances it is seen, that not only is the loss of water, owing to 
evaporation, retarded by the cuticular covering, but also that the vitality or ger- 
minating power of the tuber is destroyed by its removal ; and further, that the 
removal of the outer delicate cuticle has much the same effect in promoting 

To what extent these portions of meat and fish might otherwise be altered, and their nutritive 
quality impaired, is a question I am not prepared to answer. I may mention that white of egg, 
which, on thorough desiccation at a low temperature, is again for most part soluble, appears, if long 
kept, to become insoluble, judging from a trial of some put by after desiccation in 1852, and recently 
examined. 

* Now, August 5, No. 1, where least exposed to light, has become greenish ; where most 
exposed, brownish green. 

No. 2 has become dark brown, almost black, and has acquired a crescentic form, contracted, 
without being shrivelled. 

No. 3 has become of a light brown, and is much shrunk and shrivelled. 

f Now, September 10, on No. 1, three small greenish sprouts have appeared tipped with black ; 
general hue the same. Nos. 2 and 3 of the same colour and appearance as before. 

I Now, December 1 , the sprouting buds of No. 1 have grown a very little, showing a very 
feeble vitality, and very slow progress. In Nos. 2 and 3 no apparent change. 

§ Now, February 2, the bud of No. 1 has grown into a stalk, with terminal greenish leaflets, 
and three lateral long roots, with delicate spongioles. 

|| Now, March 14, the tuber No. 1 is slightly shrunk; the stem from it is *9 inch in length, 
and -3 inch in diameter where thickest; is of a dark purple, and is surmounted by several small 
green leaflets ; the roots from its side, numbering five, vary in length ; the longest is 1*7 inch. 
Weighed again on the 28th of May, the tuber was only a little more shrunk; it was reduced to 
161-5 grs. The growth from it, the stem, leaflets, and other offshoots, had all a healthy appearance. 

VOL. XXIV. PART I. 2K 



120 dr davy's observations on the cuticle. 

evaporation as the removal of the whole of the integuments, and is as fatal to 
life ; the colour, too, which the tuber acquires, with change of form from its re- 
moval, are circumstances which seem worthy of note.* 

On the 26th September, two apples of the same kind, not sweet, were selected ; 
one unpeeled (No. 1), weighed 933 - 5 grs ; the other peeled (No. 2), weighed 
1051 grs. They were suspended by their stalk in a room, the temperature of 
which varied from about 80° to 55° and 50°, during the time of trial. The results 
of the weighing from time to time are given in the following table, viz., the loss 
per cent. : — 

October I. No. 1 bad lost 18 per cent , No. 2, 13-9 



11. 


55 


8-1 


1$ 


„ 61-5 


30. 


»s 


14-2 


if 


„ 80-8 


November 6. 


55 


17-7 


55 


„ 824t 


12. 


>5 


18-9 


V 




20. 


)• 


21-8 


55 




26. 


55 


24-2 


95 




December 2. 


55 


265 


35 




14 


»' 


30-1 






30. 


55 


337 


5> 





On the 30th December, No. 1 was shrivelled ; it retained its colour, a greenish 
hue, and, cut into, was found free from decay. No. 2 had become very much 
shrunk, had acquired a brown colour, and a slight degree of sweetness. 

I need not dwell further on the remarkable manner in which the dessication 
of vegetable substances preserves them from chemical change, and in many 
instances for a long period ; but I must express regret that a process so simple, 
and in other countries, especially France and the United States of America, so 
much used, is not more employed in Great Britain. By means of it, the families 
of the labouring class might secure to themselves throughout the year a greater 
variety of food at a cheap rate ; the apple for instance ; several vegetables, such 
as the carrot, potato, &c. — a variety equally recommended by two qualities, which 
happily are seldom disjoined, those of agreeableness and wholesomeness.+ 

* In another experiment, begun on 27th October 1863, the results were much the same, with 
this difference, that, on the 17th March 1864, the unpeeled potato was removed from the light into 
a dark cupboard, and covered with a small inverted porcelain jar. There it has vegetated ; it has 
shot out many branches, all but the largest of which are white ; it is of a light purple ; attached to 
them are many well-formed tubers. Now, March 15, 1865, the weight of the potato is reduced from 
what it was at first, viz., 9005 grs., to 331 grs. It has no terminal leaflets. There are seventeen 
small tubers connected with it ; all are of an oval form, like the parent tuber ; the largest is -4 inch 
in length. All of them are throwing out shoots, and they are most easily detached. 

f Its weight afterwards fluctuated a little, according to the hygroscopic state of the atmo- 
sphere. 

J Sliced apples exposed to the air dry rapidly, as do also sliced potatoes and carrots ; and if 
put up in paper bags in a dry place, they will keep fit for use for a long time. No vegetable that 
I am acquainted with undergoes change more rapidly than the sweet potato [Batatas edulis), yet 
when sliced and dried, as I have found by experience, it may be kept for years unaltered. I have 
some thus preserved, which I brought from the West Indies in 1848. 



EPICYCLOID S 



Trans Roy. Soc. Edin r Vol.IWFl.7I 



I 3 ■'■■ 
Fig. J 




A = .500 000 
B = .5 00 



oL ' /3 ■■■ J :-3 

Fig 2 




/3 :: J 

Vig. 3 



^ 



at 



/i ■■■ Z -4 
Fa 6 4- 




A ■= .521 224 
B = .+7 8 77 6 




EPICYCLOIDS 



Trans Roy. Soc I<knT Vol JW TIM 



Tig. 5 



/f -■■ 1 
Tig. 7 



A - .555 556 
B — *4r* 44-t 




A 
B 



5 000 00 
. 5 OOOOO 




Fig. 6 




cL ■■ /J ■■■■ 1-5 
Kg. 8 




■LJ<- *.Tkni!a<\ . > i~ ■■'■-> ~J<- ■ 



. t ■ 



EPICYCLOIDS. 



Trans Roy Joe. £duiT VoL.UWIlW 



oL /B ■■ 1 ■ 6 



Kg- J1 



1 6 



A - 589 335 
B -.4-10 665 




A _ .508923 
B - .491 077- 




oL ■ 12, •'■ 7 -e 
Fig . 10 




<* ■ fd ■■■ 1 -~6 



Fig. 12 




To ATLrtarUidiai iwif*- 



EPICYCLOIDS 



Trails. Roy. Soc. Zdm r Wl.HI7fl.IX. 



oL -/3 ■■■ Z ■■ S 
Fi£. 13 



oL ■ J3 ■■- 2s ■ S 
Ti&. 15 



A = . 900 000 
B - . 100 000 




A _ 862 069 
B _ .137 93] 




Fi£ . 14 




^3 .:■ z ■ -s 



1%. 16 




.<-A-KJ<&ns'-u vE<£nht»v? 



EP1 CYCLOIDS. 



Trans. Roy Soc pdmf 731 XXIV Fl. I 



a! /J •' 



Fig 



A _ .750 00 
B = .250 000 



oC /3 Z ■ ■ - 4 








A _ .714- 286 
B _ .285 714 




at ■ /3 ■■ ■ ■ 2> ■ - 6 

Fig. ZO 




rtAXJefaiston.XS&ibuyk. 






'A J. 









EPICYCLOIDS 



Trans. Roy. Joe. £duv r VoL.JW PI. II 



at /! Z • S 
H&21 



oL ■ J3 ■■■ Z ■ J 
Fi£.23 



A _ . 540 000 
E _ . 4-6 000 




A - 515 100 
E _ .484 900 




at J3 ■■■' Z ■ -S 
Fig. 22 




Fig. 2 4 




V &J.JLJolm*touE£nhi>*g>i ■ 



EPICYCLOIDS 



Trajis. 2toy Joe. £dut r VoL.inVFLJK. 



oL ■ /3 ■■ Z 



10 ■ x- ■ 7 

Fig. 25 






A _ 5 6 .9 29 
B -4 93 071 




3 



.56 8 535 
431 4-65 




Rig. 26 



ot ■ /l ■■■■ 2 ■ -7 
Fie. 2 8 





ft.K Jo hartcm. ±'3m Vu rgh 



( 121 ) 



X.— On the Contact of the Loops of Epicycloidal Curves. 

(Plates VI. to XII.) 

(Read 3d January 1865.) 



By Edward Sang, Esq. 



During the summer vacation, Mr Henry Perigal of London proposed to me 
the following problem :— 

"To determine the proportions of an epicycloid of which the loops touch each 
other." 

The solution of this problem contains some points of interest to the general 
analyst, and exhibits relations between certain trigonometric formulae and alge- 
braic equations. I, therefore, offer an outline of it to the attention of the Royal 
Society. 

Mr Perigal had obtained the solution, in a considerable variety of cases by 
the method of trial, aided by mechanical appliances, and has exhibited them in 
his beautiful series of machine-engraved epicycloids. 

1. If we suppose two radii OA and OB to turn on a common centre with 
uniform velocities, in the manner of the two hands of a 

watch, and if, at each instant, we complete the paral- 
lelogram OAPB, the opposite corner P describes an 
epicycloid. This curve may be obtained by causing the 
line AP to turn on A as a centre, while A itself describes 
a circle round ; or by causing the arm BP to turn on 
B as a centre, while B moves round the fixed centre 0. 
These are the ordinary arrangements by wheel- work. 

There are other arrangements by help of which 
epicycloids may be produced, but they all result in 
giving, for the equation of the curve referred to rect- 
angular co-ordinates, the formulae 

x = A . cos at + B . cos fit 
y — A . sin at 4- B . sin (3t 

in which A and B represent the length of the arms, a and fi their angular velo- 
cities, and t the time elapsed since both arms were in the direction OX, so that 
at and fit are the angles XOA and XOB respectively. 

2. fi being supposed to be the greater of the two angular velocities, if the arm 
OB were minute as compared with OA, the curve described by P would be nearly 
circular and slightly undulated ; as OB is augmented the waves become deeper, 
as shown in figs. 13 and 14, and when OB reaches the magnitude determined 

VOL. XXIV. PART I. 2 L 




122 MR EDWARD SANG ON THE CONTACT OF THE 

by the proportion /3 2 : a 2 : : A : B, the curve becomes flat at certain points, that 
is, the radius of curvature there becomes infinite ; this phase is exemplified in 
figs. 15, 16. When OB increases beyond this value the curve becomes sinuous, 
its concavity being turned inwards and outwards alternately, as is seen in figs. 
17, 18 ; and when OB becomes so great as to satisfy the condition (3 : a : : A : B, 
the curve becomes cusped, and assumes that form to which the name epicycloid 
is sometimes restricted ; this form is exemplified in figs. 19, 20. When the arm 
OB is made still longer the epicycloid is looped, the loops being arranged at 
regular intervals, as in figs. 21, 22 ; and if OB be made sufficiently long, the loops 
come to touch each other, as in figs. 23, 24. Mr Perigal's problem is to deter- 
mine the conditions under which this contact of the loops takes place. The loop 
may touch those adjacent to it on either side, or, if OB be made sufficiently long, 
those separated from it by two, three, or more intervals ; so that the problem 
may have more than one solution. 

3. From the very genesis of the curve it follows that the contact of the loops 
must occur either on the major or on the minor radius-vector; now the angular 
motions of the arms may be either in the same or in opposite directions, where- 
fore there are four cases to be examined. 

4. When the arms turn in the same direction, and when the contact is to be on 
the major radius-vector, we may use the formulae of Article 1, unchanged ; and 
since, at the instant of contact, the curve must touch the radius- vector OX, we 

must have both #=0, and its derivative 757=0 ; hence, if T denote the time at 

which the tracing-point is in this position, we must have 

= A . sin aT + B . sin /3T 
= aA . cos aT + /5B . cos /3T 

whence we obtain the two proportions 

a : (3 : : tan aT : tan /3T 
A : - B : : sin /3T : sin aT 

5. When the arms turn in the same direction, and when the contact is to be 
on the minor radius- vector, we have to change the sign of B in the preceding 
formulae, which are thereby converted into 



= A . sin aT - B . sin /3T 
= aA . sin aT - /SB . sin /3T 



whence 



a : 


:/3: 


: tan aT : 


tan/3T 


A 


: B : 


: sin /3T : 


sin aT 



LOOPS OF EPICYCLOIDAL CURVES. 123 

6. If the arms turn in opposite directions, we have to change the sign of /3 in 
the preceding formulae. By this we merely reverse the order of the occurrence 
on the major or on the minor radius, and thus the general condition of the con- 
tact of two loops is contained in the proportion 

a : jS : : tan aT : tan /5T ; 

in other words, we have to find two arcs aT and /3T in the ratio of a to (3, and 
having their tangents in the same ratio. 

7. If we put x for the tangent of the arc T, the above proportion becomes, 

a a a, — la — 2 o . 



a. a — 1 2 a. a. — la — 2 « — o 4 

1—1 9— X + T yj— o A X — &C. 



1 2*^1 2 



/3 /5 /3— 1 j8— 2 3 

f ^ — 1 ~2 3~~ ^ + &c - 

1 — 1 2 ^ "r 1 2 3 4"^ lV0 - 



On developing and subtracting the common term a(3z from each side, the result 
is divisible by x z , and we obtain an equation into which only the even powers of 
x enter. When a and (3 are prime to each other and both odd, the order of the 
equation, x 2 being regarded as the unknown quantity, is ^ (a + (3 — 4) ; and 
when one of them is even the equation is of the order ! (a + (3 — 3) ; and it is to 
be observed that when a + (3 is even there is always the solution T = 90°, B = A, 
which corresponds to a contact at the centre of the epicycloid. 

8. A table of the values of T and B (A being taken as unit) for all cases up to 
(3 = 10, is subjoined. These values were readily obtained by the process which I 
published in 1829 (Solution of Algebraic Equations of all orders) ; the values 
of x 2 having been taken to ten places of decimals ; and those of T and B having 
been thence computed by the ordinary seven-place tables. 

It may be noticed that the only case in which the ratio of A to B can be ex- 
pressed by integer numbers is that of a : /3 : : 1 : 5 ; this rationality being con- 
nected with the fact that 1 and 5 are the only two component parts of the perfect 
number C which express a ratio in its lowest terms. And farther, that the ratio 
of A to B is the same whether the arms turn in the same or in opposite directions ; 
this fact is exhibited in the accompanying figures. 



124 



MR EDWARD SANG ON THE CONTACT OF THE 



K 





A 


B 


Log B 




T 






3 




1000 0000 


0-000 0000 


o 

90 


00 


00-00 




4 




•915 5587 


9-963 1069 


54 


05 


41-40 




5 

5 




•800 0000 
1-000 0000 


9-903 0900 
0000 0000 


37 
90 


45 
00 


40-50 
0000 


1 


6 
6 




•696 8284 
•964 9338 


9843 1257 
9-984 4975 


43 

74 


19 
33 


4835 
38-71 




7 
7 
7 




•613 0718 

•898 7860 

1-000 0000 


9-787 5114 
9-953 6563 
0000 0000 


37 
63 
90 


02 

42 
00 


5010 
32-40 
0000 




8 
8 
8 




•545 4784 
•828 5136 
•980 4880 


9-736 7775 
9-918 2997 
9-991 4423 


32 
55 
78 


21 
38 
34 


1720 
21-84 
08-48 




9 
9 
9 
9 




•490 4087 

•762 6565 

•938 9196 

1000 0000 


9-690 5581 
9-882 3290 
9-972 6284 
0-000 0000 


28 
49 
69 
90 


43 
23 
44 
00 


3600 
4362 
2053 
0000 


■1 


10 

10 
10 
10 




•444 9490 
•703 5140 
•889 8366 
•987 5693 


9-648 3102 
9-847 2728 
9-949 3102 
9-994 5676 


25 
44 
62 
80 


48 
25 
42 
53 


58-54 
02-25 
1654 
15-78 


2 


5 




•837 3864 


9-922 9259 


55 


47 


59-35 


2 
2 


7 
7 




•972 6638 
•758 9075 


9-987 9628 
9-880 1889 


37 
66 


59 
24 


16-80 
11-65 


2 
2 
2 


9 
9 
9 

5 




•858 4477 
•984 0117 
•617 9169 


9-933 7138 
9-993 0002 
9-790 9301 


29 
50 
71 


07 
15 

52 


49-32 
45-72 
2340 


3 




1-000 0000 


0-000 0000 


90 


00 


00-00 


3 
3 


7 

7 




•876 5924 
1-000 0000 


9-942 7977 
0000 0000 


40 
90 


43 

00 


39-83 
0000 


3 
3 


8 
8 




•977 5973 
•799 5282 


9990 1600 
9-902 8338 


34 
76 


22 
32 


28-47 
1895 


3 
3 
3 


10 
10 
10 




•986 4601 
•699 6930 
•879 2330 


9-994 0800 
9-825 8758 
9-944 1040 


26 
47 
80 


42 
02 
01 


01-12 
2770 
10-72 


4 


7 




•962 3744 


9983 3441 


62 


39 


57-36 


4 

4 


9 
9 




•828 3048 
•981 0198 


9-918 1901 
9-991 6778 


32 
70 


10 
37 


43-41 
31-13 


5 


7 




1-000 0000 


0000 0000 


90 


00 


0000 


5 


8 




•968 0850 


9-985 9134 


57 


44 


4317 


5 


9 




•910 5817 


9-959 3189 


48 


02 


1795 


5 


9 




1-000 0000 


0-000 0000 


90 


00 


0000 


7 


9 
10 




1-000 0000 


0-000 0000 


90 


00 


00-00 


7 




•975 5140 


9-989 2335 


61 


43 


23-76 



LOOPS OF EPICYCLOID AL CURVES. 



125 



9. When one of the radii, say OA, becomes indefinitely large the epicycloid 
merges into the cycloid produced by carrying the centre of a revolving wheel 
along a straight line ; and the extension of Perigal's problem leads naturally to 
this one : — 

" To construct a cycloid of which the loops may touch each other." 

10. If we suppose the centre of the revolving circle to be carried along the 
axis Y with a linear velocity v, while the radius B turns with an angular velocity 
(3, the co-ordinates of the tracing-point are 

x = B . cos {3l ; y = vt + B . sin f3t 

and for the point of contact we must have 

= vT + B . sin /5T 
= v + /3B . cos jST 

wherefore all such points are determined by the solution of the trigonometrical 

equation 

/3T=tan/3T; 

that is to say, we must discover all those arcs which are equal in length to their 
own tangents. 

11. If we put v = (3=l, we obtain the following solutions for the first ten 
cases, the first of these being that of the common or cusped cycloid. 



T 


Log sec T 


B 







00 


00-00 


0-000 0000 


1-000 00 


257 


27 


12-24 


0-663 0732 


4-603 34 


442 


37 


27-57 


0-891 5209 


7-789 70 


624 


45 


36-54 


1039 4093 


10-949 88 


805 


56 


00-77 


1-149 2717 


14-101 71 


986 


40 


35-75 


1-237 7832 


17-289 54 


1167 


11 


22-88 


1-309 5424 


20-395 88 


1347 


33 


55-30 


1-371 8187 


23540 67 


1527 


51 


08-52 


1-426 2642 


26-684 82 


1708 


04 


43-65 


1-474 6296 


29-828 38 



VOL. XXIV. PART I. 



2m 



( 127 ) 



XI. — Researches on Malfatti" s Problem. By H. F. Talbot, Esq. 

(Read 20th March 1865.) 

The problem which bears the name of the Italian geometer Malfatti, by whom 
it was first proposed and solved, has long attracted the attention and exercised 
the ingenuity of mathematicians, and has been made the subject of many careful 
and elaborate researches. 

The great attention which has been bestowed upon this problem has arisen 
partly from its intrinsic difficulty, but chiefly on account of the extreme simplicity 
of the solution finally obtained by Malfatti, which seemed to open new views of 
geometrical research, and gave reason to hope that simple solutions might in like 
manner be found of many other geometrical problems usually accounted very 
difficult or insoluble. 

The problem of Malfatti offers another singularity. Although it is a question 
of elementary geometry which can be solved by a simple and elegant geometrical 
construction, yet no geometrical proof has ever been given, as far as I am aware, 
of the truth of this construction. It has been established hitherto only by a very 
elaborate use of algebraic analysis, in the course of which, however indisputable 
the result may be, all geometrical perception of its truth is lost. And yet there 
can be little doubt, it should seem, that a geometrical reason must exist for any 
simple series of facts belonging to elementary geometry. 

The necessity of calling in the aid of analysis can only arise from the true 
connection of the geometrical principles involved in the problem being imperfectly 
understood. 

I now offer to the Royal Society a purely geometrical solution of the problem ; 
and, for the sake of clearness, I have divided it into several parts, which I have 
called Lemmas. Some of these are well deserving of attention for their own sake, 
and irrespective of Malfatti's problem. When these theorems have been 
established, their combination affords a lucid proof of the truth of the solutions 
which mathematicians have hitherto only obtained by the help of analysis. 

History of the Problem. 

In the year 1803, a distinguished Italian geometer, Signor Malfatti, proposed 
the following problem in the Memoirs of the Italian Society of Sciences, vol. x. 
part 1 : — * 

* See Gergonne, vol. i. p 347. 
VOL. XXIV. PART I. 2 N 



128 MR TALBOT ON MALFATTIS PROBLEM. 

" In a given triangle to inscribe three circles touching each other, and each of 
them touching two sides of the triangle." 

He gave at the same time a remarkably simple geometrical solution which he 
had discovered, but unaccompanied by any geometrical demonstration of its truth. 
He contented himself with showing that, if we calculate the algebraic values of 
the three radii which result from the above-mentioned geometrical construction, 
these three values, when substituted in the analytical equations deduced from 
the original conditions of the problem, do in fact satisfy them, and are therefore 
demonstrated to be true. But he gives no indication of any process of reasoning 
by which he arrived at the knowledge of these values. 

In the year 1810, Gergonne proposed this problem for solution in the " Annales 
des Mathematiques," vol. i. p. 196, without knowing that it had been previously 
solved by Malfatti ; and no solution of it being sent to him by his correspon- 
dents, he took up the inquiry himself.* He makes the following preliminary 
statement : — 

" II y a plus de 10 ans que ce difficile probleme s'est offert pour la premiere 
fois aux redacteurs de ce recueil, mais bien qu'ils 1'aient attaque un grand nombre 
de fois ils n'ont pu pendant longtemps parvenir a le resoudre ni meme a s'assurer 
s'il etait resoluble par la ligne droite et le cercle 

" Ils ont cru devoir faire encore de nouvelles tentatives, et plus heureux cette 
fois que les precedentes ils sont parvenus sinon a trouver une construction du 
probleme, du moins a l'abaisser au premier degre." 

Then follows an analytical investigation, which finally gives an algebraic value 
for the radius of any one of the circles in terms of known quantities. But this 
value does not lead to any simple geometrical construction, nor is it easy to show 
that it agrees with that previously found by Malfatti, which, however, must 
necessarily be the case. 

Having succeeded to this extent, M. Gergonne did not believe the problem to 
be susceptible of much further simplification, when he first became acquainted 
with the previous researches of Malfatti. Having procured and perused the 
memoir of that author, he found that it threw no light upon the point of chief 
interest, viz., the mode of investigation by which a result so unexpectedly simple 
had been obtained.f 

Nothing further appears to have been done till the year 1820, when M. Lech- 
mutz, of Berlin, published a memoir in Gergonne's Annales, vol. x. p. 289, in 
which he succeeded for the first time in solving the problem, by a course of a p?*iori 
reasoning. His investigation is algebraical, and his results coincide with those of 
Malfatti. In the year 1826, Steiner, a distinguished geometer of Berlin, threw 
an entirely new light upon the problem, by giving, in Crelle's Annals (vol. i. p. 

* See Gergonne, vol. i. p. 343. f Ibid. vol. ii. p. 60. 



MR TALBOT ON MALFATTl's PROBLEM. 129 

178), a geometrical construction of singular simplicity, but entirely unaccompanied 
with proof. His solution is as follows : — 

Let ABC be the triangle in which it is required to inscribe three circles touch- 
ing each other, and each of them touching two sides of the triangle. Bisect the 
angles A, B, C, by three lines AO, BO, CO, which will meet in the point 0. In 
the three triangles AOB, BOC, COA, inscribe three circles, touching the sides of 
the given triangle in the points D, E, F, which letters will serve to denote those 
circles respectively. From the point of contact D, draw a line DG, touching the 
circle E on its inner side. Similarly from the point of contact E, draw a line EG 
touching the circle D, on its inner side. And let DG, EG, intersect in G. Then 
we have a trapezium BDEG, and Steiner affirms, first, that a circle can 
always be inscribed in this trapezium ; and, secondly, that the circle so inscribed 
will be one of the three required circles. 

But no doubt a difficulty will be observed immediately. Steiner directs that 
the line DG shall be tangent to the circle E ; and plainly there is no reason why 
the circle E should be selected rather than the circle F. But the reply to this 
is, according to Steiner, that if the line DG touches the circle E, it will also 
necessarily touch the circle F. 

But of this most remarkable theorem he gives no demonstration whatever, 
although there is assuredly no theorem in the whole of geometry which has less 
claim to be considered as an axiom. Moreover, he affirms that the same line, 
DG, touches two of the required circles of the problem, at the point where they 
touch each other. This being admitted, the construction of the problem follows 
at once, as it is only requisite to describe a circle touching AB, BC, two sides 
of the given triangle, and also the known line DG, and this circle will be one of 
the three circles required, the others being found with equal facility. 

Steiner's solution, therefore, would have left nothing more to be wished for, 
if it had been accompanied with a demonstration. But of such his memoir con- 
tains not a single syllable. He says, indeed (page 178), that this solution of a 
difficult problem shows "the fruitfulness of the preceding theory;" but the 
critical researches of subsequent inquirers have not failed to discover the singular 
circumstance, that there is no connection whatever between this solution of 
Malfatti's problem and the theories set forth in the preceding part of Steiner's 
memoir. 

The great simplicity and elegance of this solution discovered by Steiner 
rendered a demonstration of it very desirable, which was at length accomplished 
by Zornow of Konigsberg, in Crelle's Annals for 1833 (vol. x. p. 300). The 
demonstration of Zornow is remarkably elegant, but it chiefly depends upon 
some very dexterous algebraic transformations, in the course of which, how- 
ever, all perception of a geometric proof of the construction necessarily dis- 
appears. 



130 MR TALBOT ON MALFATTl'S PROBLEM. 

In the following year, PlUcker of Bonn resumed the subject in Crelle's 
"Annals," xi. p. 121. His memoir, which bears date October 1831, throws a 
great deal of new light upon the subject. His object was, like that of Zornow, 
to demonstrate the truth of Steiner's construction, in which attempt he succeeds 
up to a certain point, by a well-conducted train of geometrical reasoning ; but 
beyond that point he cannot proceed without the help of analysis. In fact, he 
shows geometrically that there exists a certain point within any given triangle 
ABC (see former figure), which possesses the property, that if AO, BO, CO, are 
joined, and three circles are inscribed in the three triangles AOB, BOC, COA, as 
in that figure, then the line DG will touch both the circles E, F, and also two of 
the required circles. It remained to discover what point of the triangle the point 
was, and to verify Steiner's assertion that it was the centre of the inscribed 
circle, or that the lines AO, BO, CO, respectively bisect the three angles of the 
given triangle. But of this capital point Plucker was unable to find any 
geometrical proof. He has recourse, therefore, to a very free and prolix use of 
trigonometry and algebra, through which I doubt whether any of his readers 
have had the courage to follow him, but which finally conducts him to the con- 
clusion that Steiner's assertion is true. It will be observed that Plucker's 
memoir, though published subsequently to that of Zornow, preceded it in point 
of date ; that of Zornow being dated in October 1832. He was, therefore, the first 
who succeeded in demonstrating Steiner's theorem. Plucker concludes his 
memoir with the following remarks upon the mode in which Steiner has treated 
the question : — * 

" The construction which I have given is essentially the same with that pro- 
posed by Steiner in vol. i. of this journal, p. 178. There is, however, at that 
place no indication of a demonstration. The introductory words of the author— 
' to shorn the fraitfulness of the theorems set forth in paragraphs 1 , 2, 3, by a suitable 
example, we add the geometrical solution, and also a greater generalisation of 
MalfattV s problem, omitting the proof ' — might cause a person who (as I must con- 
fess to be my own case) has no idea how the construction of that problem can 
depend upon the well-known theorems explained in the above quoted paragraphs 
concerning points of similitude, &c, &c , to think that the given construction is 
not proved."! 

I have said that Plucker's recourse to a difficult and very prolix analysis in 
order to justify the assertion that is the centre of the inscribed circle, is the 
weak point of his able investigation. He has admitted this himself, for he says 
(p. 126), " So soon as this theorem is brought into its proper connection there 

* Vol. xi. p. 126. 

f Die einleitenden Worte des Verfassers; " Um die Fruchtbarkeit," &c. &c, konnten demjeni- 
gen, der, wie ich von mir bekennen muss, keine Idee davon hat, wie die Construction, &c, &c 
den G-edanken aufdrangen, dass die gegebene Construction nicht bewiesen sei. 






MR TALBOT ON MALFATTI S PROBLEM. 



131 




Fig. 1. 



can be no doubt that an easier proof will be found of it." And he adds a wish 
for "a simple geometrical proof." 

In the demonstration which I now submit, I shall follow Plucker's geometrical 
proof in a general way, up to the point where he breaks 
away from geometry into the regions of analysis, and then 
give a proof, by geometry alone, of the remaining portion 
of the investigation. 

Lemma 1. — If a circle is inscribed in a triangle, the 
difference of the sides equals the difference of the seg- 
ments of the base. 

This is evident. D, E, F, being the points of contact, 
AB — AC = BE — CF = BD — DC. 

Lemma 2. — Let two circles touch each other at 0, and let BFGC be their 
common external tangent, and AOD their 
common internal tangent. Let A be any 
point in the tangent AOD, and let AEB, 
AHC, be drawn touching the circles ; then 
if a circle be inscribed in the triangle ABC, 
it will touch the base BC at D. 

Demonstration. — We have manifestly the 
equal tangents AE = AH, DF = DG, BE 
= BF, and CG = CH. Therefore AB - 
AC = BE - HC = BF - GC = BD - DC. 
Therefore by Lemma 1 the inscribed circle touches the base in D. 

Lemma 3. — This is only another case of Lemma 2, when the point A is taken 
so near to that the tangents AE, 
AH, diverge from the base BC, but 
their prolongations AB, AC, intersect 
the base at B, C. 

In this case also we have the equal 
tangents AE = AH, DF = DG, BE = 
BF, and CG = CH. Therefore AB - 
AC = BE - HC = BF - GC = BD - 
DC. 

Lemma 3 is the case which occurs 
in the solution of Malfatti's problem, but as the same demonstration applies to 
Lemma 2, I have given both of them. 

Lemma 4. — If tangents of equal length are drawn to acircle, the locus of their 
extremities is a circle concentric to the first. 

Lemma 5.— Let there be two circles A, B, and let RS and its equal RS be their 
two common internal tangents; then if OP, OQ are two tangents drawn from 





VOL. XXIV. PART I. 



2o 



132 



MR TALBOT ON MALFATTI S PROBLEM. 



any point O not situated either in RS produced, or in RS produced, OQ — OP 

is not equal to RS. 

Demonstration. — Let the points A, B, be 
the centres of the given circles. From 
centre A with radius AO describe a circle 
cutting RS produced in Z. Then by Lemma 
4, OQ = ZS, whence OQ - OP = ZS - OP. 
But OP is not equal to ZR, because lies 
on the circumference ZO, which is not con- 
centric to the circle B. Therefore OQ — OP 
is not equal to ZS — ZR ; therefore it is not 
equal to RS. Q. E. D. 

Corollary.— If OQ — OP is equal to RS, 
must either lie in RS produced or in RS 
produced. 
Lemma 6. — Let A, B, C, be three circles. Let DE be the internal common 




Fig. 4. 




Fig. 5. 



tangent of A and B ; FG of B and C ; and HI of C and A. Then if these three 
tangents, when produced, meet in a single point 0, 

DE = FG + IH 

or the greatest common tangent equals the sum of the two others. 
For, 

IH = 01 - OH = OD - OG = DE - FG. 



MR TALBOT ON MALFATTI S PROBLEM. 



133 




Lemma 7. — Let A, B, C, be three circles. Let DE be the external tangent 
of A and B. Let FG be the external tangent of A and C ; and let HI be the 
internal tangent of B and C. Then if these 
three tangents, when produced, meet in a single 
point 0, 

FG - DE = HI 
For, 

FG - DE = OG - OE = 01 - OH = HI. 

Lemma 8. — If three internal common tan- 
gents of three circles meet in a point 0, their 
other three internal common tangents meet in 
another point P. 

Demonstration. — In figure 5, suppose the 
common tangents meeting in to be effaced, 
and replaced by the three other internal com- 
mon tangents, it is required to show that these 
also meet in a point. 

Let two of them, viz. those touching the Fig. 6. 

circle A, meet in the point P. Denoting the new tangents by the same letters 
as before, but accentuated, we have of course 

DE = DE, FG = FG, HI = HI 
Now we proved in Lemma 6 that 

DE = FG + HI, or ED - HI = FG 
therefore we have 

ED - Hi = FG 

The new common tangents meeting in P will be PED, PHI ; but these have 
a part which is equal in each, namely PE' = PH', which are tangents to the same 
circle A. Therefore subtracting this part, we have 

PED - PHI = ED - HI 

which we proved to be equal to FG. 

Therefore P is a point from which tangents PD', PI have been drawn to the 
circles B and C, and their difference has been found equal to FG the internal 
common tangent of B and C. Therefore by the corollary to Lemma 5, P is a point 
in F(jt produced. Q. E. D. 

Lemma 9. — If two external and one internal common tangents of three circles 
meet in a point O, the three other corresponding tangents meet in another 
point P. 



134 MR TALBOT ON MALFATTl's PROBLEM. 

The demonstration of this is the same as the last, employing Lemma 7 instead 
of Lemma 6. These theorems may be called Plucker's tangents, from the name 
of their discoverer (Crelle's Annals, torn. xi.). It is evident that there are several 
more cases besides those considered in Lemmas 6, 7, 8, 9; but I omit them, 
because they are not required for the solution of Malfatti's problem. The 
demonstration of each would be nearly in the same words. 

Lemma 10. — If three lines issue from a point A, and contain the angles DAX, 
EAX, which may be called 6 and <P ; and if two circles, with centres B and C, are 




Fig. 7. 

inscribed anywhere in these angles, touching the outer sides at D and E ; then if 
DE is joined, the intercepted chords DF, GE are in a contant ratio; namely, in 
the ratio of tan | 6 to tan \<p. 

Demonstration. — Join BD, and draw the perpendicular BH, dividing the 
chord DF into two equal parts. Draw AI perpendicular to DE. 

Then, since the triangles ADI, BDH are similar, 

AD : AI : : BD : DH 
. • . DH = AI . ~ = AI . tan £ 
. • . chord DF = 2 AI . tan \ 6 
By similar reasoning it may be shown that chord GE = 2AI tan \ $ 

. • . DF : GE : : tan £ 6 : tan \ <p 

Corollary 1.— If 6 = <p t DF = GE. That is :— " If the circles subtend equal 
angles at A, the intercepted chords are equal." 



MR TALBOT ON MALFATTl'S PROBLEM. 135 

Corollary 2. — If 6 is greater than </>, then DF is greater than GE. 

Lemma 11. — If any angle DAE is bisected by the line AX, and two circles 
are inscribed anywhere in the semi-angles DAX, EAX touching the sides at D 
and E ; then the tangent DK is equal to the tangent EL. 

Demonstration. — Join DE. We have shown in Lemma 10 that in this case the 




Fig. 8. 

intercepted chords DF, GE are equal. Subtract them from the whole line DE, 
and the remainders DG, EF will be equal. Therefore 

DG . DE = EF . ED . \ DK 2 = EL 2 
and 

.-. DK = EL 

Corollary. — Conversely, if DK = EL it follows that the angle DAX = angle 
EAX. 

For, if those angles are not equal, let DAX be the greater. Then because 
the angle DAX is greater than the angle EAX, the chord DF is greater than the 
chord EG (by Lemma 10, corollary 2). Subtract them successively from the 
line DE, and the remainder EF will be smaller than the remainder DG, therefore 
EF . ED is less than GE . DE ; therefore EL 2 is less than DK 2 ; and EL is less 
than DK. But on the contrary EL = DK by hypothesis. Consequently it is not 
true that the angle DAX is greater than the angle EAX. In the same way it 
is shown that it is not less ; consequently it is equal to EAX. Q.E.D. 

Lemmas 10 and 1 1 are particular cases of a much more general theorem which 
I propose to give on another occasion. In the first nine Lemmas I have chiefly 
followed Plucker, but have endeavoured to make his demonstrations more 
rigorous by going more into detail than he has done. But Lemmas 10 and 11, 

VOL. XXIV. PART. I. 2 P 



136 



MR TALBOT ON MALFATTI S PROBLEM. 



and the more general theorem of which they are particular cases, are original ; at 
least I am not aware of their having been published elsewhere. They supply the 
link that was missing in Plucker's investigation, and singularly facilitate the 
demonstration of Steiner's elegant construction. 

By the help of the preceding Lemmas, we can show the truth of that con- 
struction in the following manner : — 

Malfatti's Problem. 

It is required to inscribe in the triangle ABC three circles touching each other. 

and each of them touching two sides 
of the triangle. 

Solution. — Suppose the thing done, 
and the three circles A', B', C, found, 
it is plain that their three internal 
common tangents meet in a point N, 
and bisect the external tangents GH, 
IJ, KL. 

Produce the lines EN, FN beyond 
the point N until they meet the base 
BC in two points Q, R. Then if in 
the triangle QRN so formed, we in- 
scribe a circle which may be * called a, it will touch the base BC in the point D 
(by Lemma 3). 

By an exactly similar process we obtain a circle (3, touching DN, EN produced, 
and the side AC in F ; and a circle 7 touching DN, FN produced, and the side 
AB in E. 

A 





Fig. 10. 



* I have called it a, because it stands opposite to the angle A of the original triangle, 
larly for the names of j3 and y. I have called a, j3, y the secondary circles. 



Simi- 



MR TALBOT ON MALFATTI S PROBLEM. 137 

This will be seen better by referring to fig. 10, in which, to avoid confusion, I 
have only represented one of the required circles B', and the two secondary circles 
a, 7, which belong to it. I have represented the prolongations of the three 
tangents DN, EN, FN by dotted lines. The secondary circles touch these dotted 
lines, and also touch the sides of the triangle at D and E, where the tangents 
intersect them. A simple inspection of the figure suffices to show that the 
tangent DY drawn from D, which touches both the circles B' and 7, is the sum 
of two parts, which equal the external tangents DG and EL respectively. And 
that the tangent EZ, drawn from E, which touches both the circles B' and a, is 
the sum of two parts, which equal the external tangents EL and DG respectively. 
Therefore, these two tangents DY, EZ are equal to each other, since each of them 
equals DG + EL. 

But the three lines DN, EN, FN meet in one point at N ; that is, the three 
internal common tangents of the circles a, (3, 7 meet in one point. Therefore, by 
Lemma 8, their other three common tangents must also meet in one point, 
which point may be called 0. 

Moreover, the line DN produced is the external tangent of the circles B' and 7 ; 
and EN produced is the external tangent of the same circle B' and circle a ; and 
(as we said before), FN produced is the internal tangent of the circles a and 7. 
But DN, EN, FN concur in a point ; that is, two external and one internal common 
tangents of the circles a, 7, and B' concur in a point. Therefore, by Lemma 9 the 
other three corresponding tangents of those circles meet in a point. And it is easy 
to see what that point is. For, the second external common tangent of the circles 
B' and 7, is AB, one of the sides of the given triangle ; and the second external 
common tangent of the circles B' and a is BC, one of the sides of the triangle. 

But we know the point of concourse of AB and BC, to be at B, one of the 
vertices of the triangle. Consequently, we attain this important result, that the 
second common internal tangent of the circles a and 7 passes through the angular 
point B of the triangle. In a similar way, it may be shown that the second 
common internal tangent of the circles a and (3 passes through the angle C ; and 
that the second common internal tangent of the circles (3 and 7 passes through 
the angle A. 

These three tangents are therefore three lines proceeding from A, B, C, the 
three angles of the given triangle, and meeting in a single point (which a few 
lines previously we named 0). Now Steiner affirms that this point is the 
centre of the inscribed circle of the given triangle ABC ; and this is the theorem 
which Plucker and other geometers have been unable to prove except by the 
use of analytical methods of investigation. But here we call to our assistance 
the Lemma 11, which we have demonstrated above; and we proceed as follows. 
Since we have shown that the line BO touches the circle a, and also the circle 7. 
And since we have also shown that the line DY drawn from the point of contact 



MB TALBOT ON MALFATTl's PBOBLEM. 

D to the circle 7 , is equal to the line EZ drawn from the point of contact E to 
ton h the ctrcle a. Therefore by the corollary to Lemma 11. the line BO neces- 
sarily b.sects the angle B of the original triangle. Similarly it is shown that 
CO Insects the angle C, and that AO bisects the angle A. Therefore oTt h 
centre of the mscnbed circle of the triangle ABC : -which is Stub's Theorem 
The solution of Malfatti's Problem is therefore as follows — 

Bisect the angles of the triangle ABC, by the lines AO, BO, CO In 
two of the smaller triangles thus made AOB, BOC, inscribe the circles 7 and « 
From D, the pomt of contact of „ with the side BC, draw a line DY, touchin" the 
circle y. Then DY will touch one of the required circles also; which c ^0 
touches AB, BC, two sides of the triangle, and is therefore whollv deemed 



( 139 ) 



XII. — On the Law of Frequency of Error. By Professor Tait. 

(Read 3d January 1865.) 

1. It has always appeared to me that the difficulties which present themselves 
in investigations concerning the Frequency of Error, and the deduction of the 
most probable result from a large number of observations by the Method of Least 
Squares (which is an immediate consequence of the ordinary " Law of Error"), 
are difficulties of reasoning, or logic, rather than of analysis. Hence I conceive 
that the elaborate analytical investigations of Laplace, Poisson, and others, do 
not in anywise present the question in its intrinsic simplicity. They seem to me 
to be necessitated by the unnatural point of view from which their authors have 
contemplated the question. It is, undoubtedly, a difficult one ; but this is a strong 
reason for abstaining from the use of unnecessarily elaborate analysis, which, 
however beautiful in itself, does harm when it masks the real nature of the 
difficulty it is employed to overcome. I believe that, so far at least as mathe- 
matics is concerned, the subject ought to be found extremely simple, if we only 
approach it in a natural manner. 

2. It occurred to me lately, while I was writing an elementary article on the 
Theory of Probabilities, that such a natural process might possibly be obtained 
by taking as a basis one of the common problems in probabilities, viz. : — To find 
the relative probabilities of different combinations of mutually exclusive simple events 
in the course of a large number of trials. 

3. In fact, this is really the basis of Laplace's investigation, an elegant, but 
very troublesome piece of analysis. With the view, apparently, of attaining the 
utmost possible generality, he considers an error to be made up of an infinite 
number of contributions, each from a separate source. But he assumes at start- 
ing, that these separate contributions are as likely to be of one magnitude as 
another, which is, to say the least, questionable ; as it seems to be inconsistent 
with the result finally arrived at. For instance, by far the larger part of the pro- 
bability of a given finite error is thus made to depend upon a great number of 
infinite positive contributions, combined with a proper allowance of infinite 
negative ones. Now, though it is not a harsh assumption to suppose that finite 
effects should be, in certain cases, the results of additive and subtractive opera- 
tions with infinite quantities, it does appear unlikely in the extreme, that finite 
effects should be due to such operations in a far greater measure than to operations 
with finite quantities. It is true that Laplace subsequently shows that the same 
law will be arrived at by assuming any law of probability for the contributions to 

VOL. XXIV. PART I. 2 Q 



140 PROFESSOR TAIT ON THE LAW OF FREQUENCY OF ERROR. 

the error from each separate cause, provided positive and negative errors of equal 
amount are equally likely ; but it is the complexity, not the sufficiency, of his 
processes, which I think requires attention. 

4. Gauss' investigation is founded on the assumption, that the arithmetical 
mean, of the results deduced from equally trustworthy observations, is the most 
probable value of the quantity sought. So far as I can see, Ellis* has satisfactorily 
shown that this, however apparently natural, is not justifiable as an a priori 
assumption. In fact, it would seem that we have no right to assume that, be- 
cause errors of equal magnitude and opposite signs are equally likely, their sum 
will vanish in a large number of trials, any more than that the sum of their third 
or fifth powers will vanish. Why the first powers should be chosen, appears to 
arise from the extreme simplicity of the requisite operations ; yet, though com- 
plexity of calculations is undesirable, it must be submitted to, if necessary for the 
evolution of truth. The principle of the arithmetical mean has been adopted, 
among a multitude of others equally likely, just as we might suppose a calculator 
to insist on gravity varying as the direct distance instead of its inverse square, on 
the ground that the problem of Three Bodies would then become as simple and 
its solution as exact, as they are now complicated, and at best only approximate. 
" La nature ne s^est pas embarrassee des diffiadtes d" 1 analyse, elle n'a evite que la 
complication des moyens" in the words of Fresnel. 

5. It is with some hesitation that I communicate the present paper to the 
Society ; for I have not devoted much time to the study of the Theory of Proba- 
bilities ; and I know well how easy it is to fall into the gravest errors of reason- 
ing on such a subject, from the fact that D'Alembert, Ivory, and many others, 
have published investigations and proofs (sometimes in its most elementary 
parts), which are now seen to be entirely fallacious. 

6. I proceed to show how I think the principle, above (§2) enunciated, may 
be applied. The most direct method would be, of course, to assume any one set 
of causes of error whatever, and to determine what will, in the long run, be the 
chance of each separate amount of error as due to their joint action. Supposing 
this to be determined, let us try to combine the probabilities of error from any 
indefinite number of sets of possible causes ; and, if this process should lead to a 
definite law of error, such will be the law to which, by an inverse application of 
the Theory of Probabilities, we should expect each separate observation to be 
subject. But this process, which is analogous to that of Laplace, though not iden- 
tical with it, cannot easily be carried out, for it essentially involves in its first 
steps the assumption of a law of error which it is the object of the investigation 
to determine. We must try a less direct method. 

7. We shall, therefore, investigate what must be, in the long run, the chance 

* Cambridge Phil. Trans, viii. p. 205. 



PROFESSOR TAIT ON THE LAW OF FREQUENCY OF ERROR. 141 

of any combination whatever of independent events, and consider the deviation of 
this combination from the most probable combination as the Error, and the ratio of 
its probability to that of the most probable combination, as the function which 
expresses the Law of Error. If we find, as we proceed, that the law thus arrived 
at, is (in form at least) totally independent of the number, variety, &c, of the 
several simultaneously acting causes, we shall thus have a very strong argument 
in favour of the correctness of the process ; whose real difficulty, be it remembered, 
is logical and not mathematical. The mathematical processes to be employed 
below are, of course, known, and will be found in most treatises on Algebra ; 
but, for the present application, it will be convenient to put them in a form 
slightly different from the usual one. 

8. Taking the simplest case, let us suppose a bag to contain white and black 
balls, whose numbers are as p : q, where p + q = l. The chance of drawing a 
white, and (3 black, balls in n ( = a + /3) drawings, replacing before each drawing, 
and disregarding the order in which they appear, is, — 

v*<f (i) 



13 



This is a maximum, when a : j3 : : p : q; which, when n is indefinitely great, can 
always be exactly attained. This maximum value is, — 



\pn \qn 

The ratio of these two numbers is, — 



p l " l q^ (2) 



&M P -p*<r*> ( 3) 

Now, according to the principle above assumed, we must treat a —pn, the devia- 
tion from the most probable result, as measuring the error in some observation, 
while the expression (3) measures the probability of it, as compared with that of 
the most probable result. To introduce the ordinary notation, let x be the error, 
and y the (indefinitely small) probability of that error ; then, A and m being 
constants, — 

a.—pn = mw, ...... (4) 

while y may be expressed as the product of (3) into A, that is, by (4), 

y = A , I— |— p mx q- mx ... (5) 

\pn-\-mx \qn — m.r 

When n is a large number, the value of this is easily found from Stirling's 
Theorem, viz.— 



1.2.3 . . . . n = |n 



= ^27r^ + V"(l + T ^+&c.) 



U2 PROFESSOR TAIT ON THE LAW OF FREQUENCY OF ERROR. 

where the inverse powers of n may be neglected if n is large. For (5) thus be- 
comes, 

_ A (pn)P n + $ + mx (qn)V n + l- mx 



= A 



(pn + mx)P n + mx + $(qn- mx) 2" ~ mx + i 
1 



pn + mx + i , N qn-mx+i 



\ pn) \ qn) 

Hence, logy — log A= — (pn + mx + %) log(l + — ) — (qn — mx + %) \os (l — --\ 

, . . ( mx m 2 x 2 m 3 x 3 „ ) , , . { mx m 2 x 2 m 3 x 3 „ ) 

_m 2 x 2 (I 1\ mV / 1 _1\ _m i q i (l 1 \ „ 

~~ 2w Vp ?/ 6n 2 U 2 9 2 j 12n 3 V/> 3 + <zV C ' 

mcc / 1 1\ mV / 1 1 \ 

-o" ( ) +-nr(-2+^t)+ &c - 

Jn \ p <? / 4rr \p~ q~ ) 

The first term of this expression is finite when mx is of the order n h ; and in 
this case the other terms in the first line are infinitely small, being of the orders 
n~ *, n~ \ &c. respectively. The latter remark applies to the second line of the 
expression, which depends upon the ^ in the exponents. When mx is of an order 
higher than »*, it is obvious from the undeveloped form that the expression 
must be infinitely large, and negative. Hence, generally, we may neglect all but 
the first term, and we have therefore 

m 2 x 2 

,/ = Ae~2pT n 

= A€~ fLx2 (6), 

which is the ordinary expression. 

9. This shows that, as is well known, the chance of a result differing x from 
the most probable combination is, in this very simple case, represented by a number 
proportional to e — ^ times that of the most probable event. But if we now con- 
sider, not one but, any number of causes conspiring to produce the observed result, 
we find that the law is still precisely the same in form, and this whether the most 
probable event be the same as regards each cause or not. And it is this fact which 
appears completely to justify the proposed method of regarding the question. 

10. For, if the various causes all tend to produce the same most probable 
event, its probability will be, by (6), 

a = A t A 2 A 3 . . . . A„ (7) 

while that of a result, whose error is x, will be 

2/=.Ws .*-..* = ae-^ + ^ + • • • • + ^> 2 = a f - >to2 . . (8) 
(where M=/m 1 + /jl 2 + /jl 3 + .... +/u„) 
which is the same form as (6). 



PROFESSOR TAIT ON THE LAW OF FREQUENCY OF ERROR. 143 

If the most probable result, as depending on the several sets of causes, be 
different for each, the formula (6) becomes, for any one cause, 

3, = A6-^-*> 2 . . . ' . . (9), 

where A is the (small) chance of the most probable result, which is, of course, x = y. 
The chance of any particular value of x, as due to the simultaneous action of 
all the causes, is now 

y = A x .... A v €-^ x -^ 2 ~ •■■■ ~i**-v# . . (10), 

which may, of course, be put in the form 

y = % € -M(*-r? (11); 

where the most probable result is now 







X = Y- 


% + A* 2 + • • • • 


■ ) 
+ /*>* 






while 




(where, as 


. . A v e- ( ^> Z+ 
before, M = fh x + ^ 2 + 


+ fx.,y 2 ) + Mr 2 
. . . . +/!*,) 






is its 
If 


probability. 

we take this as our point 


of departure for the error x, 


we 


must write x for 


x— r, 


and we have 




GH^— MX 2 






. . (12), 



for the form of the law of error, which is precisely that of (6) deduced from 
the simplest conceivable case. 

11. Another remarkable confirmation of the validity of the process suggested 
above, is to be found in the fact that not only are the curves expressed by equa- 
tions such as (6) and (9) compounded, by multiplication of corresponding ordinates, 
into another of the same class, whatever be the positions of their axes of symmetry, 
but that the same principle holds good in three, four, &c, dimensions also. 

Thus, any number of hills on the plane of xy, represented by equations such as 

f-Ae-tf-^+M 1 ] ..... (13), 

give, by multiplication of their corresponding ordinates, another hill of the same 
general form, the values only of the constants being changed. 

[Many curious geometrical results may be derived from this construction. 
One of the most singular is the fact that the projection on x y of the line of inter- 
section of any two surfaces whose equations are of the form (13) is a circle, and 
that another such surface (viz., that whose ordinates are mean proportionals 
between those of the former) can be described, passing through the curve of 

VOL. XXIV. PART I. 2 R 



144 



PROFESSOR TAIT ON THE LAW OF FREQUENCY OF ERROR. 



double curvature of which this circle is the projection. But, besides being 
foreign to our subject, these theorems follow at once from well-known properties 

12. Returning to equation (12), it is obvious that a and M must be connected 
since we have to satisfy the condition that the probability that the error lies 
between infinite positive and negative limits is certainty. Hence, as we may 

'••••. (14) 

for the chance that the error lies between x and x + 8x- we must have 

+ 00 



«/v 



-Mz=, 

ax - L • (15), 

But we know that 






00 



-J- 00 



which reduces (15) at once to the form 



M- 1 • • • (16), 

the required relation. 

13. It is obvious from (12) that large errors hare less probability when H is 
large ; that is when h is small, if we put 



M 4 



Henee h becomes an indication of the comparative accuracy of the process whose 

zz::zT ms ' and " is thus desirawe to retain jt in *• «££z 

By (16) we have 



and therefore, by (14), we obtain 



h\/ 



7T 



1 ~- 

Ox 



/i\Ar 



foi he hance that the error lies between • and m+tm , the usual expression 

14. It only remains that we give an idea of the accuracy with which this law 
of error is approximated to, in cases such as we have assumed as the ba si of 
our reasoning even in a very small number of trials. For this purpose we ke 
the case of 20 'tosses of a coin. Here the most probable result is, of comse 10 

S £.",£ " "^ " ^ ™ — — ations^tn: 



PROFESSOR TAIT ON THE LAW OF FREQUENCY OF ERROR. 145 

If we erect these as ordinates at successive distances, each equal to unit, along a 
line, we may graphically represent their relative values by a curve drawn, libera 
mann, through their extremities. The area of this curve will evidently approxi- 
mate to unity, which is the exact value of the sum of the areas of the rectangles 
of unit breadth, each of which is bisected by one of the ordinates laid down from 
the expansion. 

To find the corresponding curve of error, notice that the maximum ordinate is 

20 . 19 11 1 184756 



2 10"2 20 "1048576 



= 0-1762. 



Taking this as the value of ■,,— we have for (12) the expression 



1 



v = x € 10 ' 253 (17). 

y 5-675 . v ; 

The following table shows a few of the values of y from this formula, compared 
with the corresponding terms in the binomial : it is sufficient for our purpose, as 
it would not be worth while to take the trouble of calculating the areas of the 
curve of error corresponding respectively to the rectangles above mentioned. 



X. 


y from (17). 


y from Binomial. 


Difference. 





0-1762 


0-1762 


o-oooo 


1 


0-1598 


0-1602 


-0-0004 


2 


0-1193 


0-1201 


-0-0008 


3 


0-0733 


00739 


-0-0006 


4 


0-0370 


0-0369 


+ 0-0001 


5 


0-0154 


0-0148 


+ 0-0006 


6 


0-0053 


0-0046 


+ 0-0007 



15. Nothing is better calculated to show the general soundness of the method 
we have adopted in this paper, than the fact of the excessive closeness of the 
above approximation : the case having been specially chosen as one in which we 
could hardly have expected more than a rude resemblance to the law of error. 



( 147 ) 



XIII. — On the Application of Hamilton's Characteristic Function to Special Cases 

of Constraint. By Professor Tait. 

(Read 20th March 1865.) 

1. One of the grandest steps which has ever been made in Dynamical Science 
is contained in two papers, " On a General Method in Dynamics" contributed to 
the Philosophical Transactions for 1834 and 1835 by Sir W. R. Hamilton. It is 
there shown that the complete solution of any kinetical problem, involving the 
action of a given conservative system of forces, and constraint depending upon 
the reaction of smooth guiding curves or surfaces, also given, is reducible to the 
determination of a single quantity called the Characteristic Function of the 
motion. This quantity is to be found from a partial differential equation of the 
first order, and second degree ; and it has been shown that, from any complete 
integral of this equation, all the circumstances of the motion may be deduced by 
differentiation. So far as I can discover, this method has not been applied to 
inverse problems, of the nature of the Brachistochrone for instance, where the 
object aimed at is essentially the determination of the constraint requisite to pro- 
duce a given result. It is easy to see, however, that a large class of such 
questions may be treated successfully by a process perfectly analogous to that of 
Hamilton; though the characteristic function in such cases is not the same 
function (of the quantities determining the motion) as that of the Method of 
Varying Action. 

2. It is unnecessary to enter into any great detail with reference to the 
present subject; because any one who is familiar with Hamilton's beautiful 
investigations will have no difficulty in applying them, with the requisite slight 
modifications, to the subject of this paper. I shall therefore content myself 
with a brief explanation of the application of the method to the problem of the 
Brachistochrone, and a mere indication of some other curious problems which 
are easily solved in a similar manner. 

3. The problem of the Brachistochrone for a single particle is. in its simplest 
form, as follows: — 

Find the form of the {smooth) constraining curve along which a particle will pass, 
under the action of a given conservative system of forces, from one given point to 
another in the least possible time, the initial velocity being given. 

The problem may easily be complicated by supposing, for instance, the 
terminal points not to be definitely assigned, but to lie each on a given surface : 

VOL. XXIV. PART I. 2S 



148 



PROFESSOR TAIT ON THE APPLICATION OF HAMILTON S 



still farther, by supposing the initial velocity to depend, according to some given 
law, upon the coordinates of the initial point, and so forth. But such compli- 
cations introduce analytical difficulties of the quasi-arithmetical kind merely, 
not of a physical nature ; and we leave them to those who are curious in such 
matters. 

4. In symbols, if t be the time of passing from x ,y Q ,z to z,y, z, we must 
have 



ds 
v 



a minimum: subject to the sole condition 

w 2 = 2(H-V) 

where H is the whole energy, and V the potential of the system of forces on 
unit mass at the point x, y, z. 
Hence, taking the variation, 

<x _ C(d8s dsdv\ 
~ J V v v' 2 )' 

But dsdSs = dxddx + dyddy + dzddz ; 

and vdv = 8(K - V) = X8x + Y8y + Z8z + §E, 

if X, Y, Z be the component forces on unit mass at x, y, z. Thus we have 



where the whole, integrated or not, is to be taken between the given limits. 

If the limits and the initial velocity be fixed, the first part of the expression 
for St disappears ; and, that the integral may vanish, we must have 



*(~i) +" ss °' 



(A). 



with similar equations in y and z. This is simply the ordinary result given in 
treatises on kinetics. 

But if we consider the effect of the alteration of the limits, or of the initial 
energy, we have 



CHARACTERISTIC FUNCTION TO SPECIAL CASES OF CONSTRAINT. 149 
8t 1 dx dr (\ dx s 



or _ 1 dx Or /l dx\ 



"o 
&c. &c. 



and §!_=- f *• 

x o> Voi z o 

/ 

5. Hence, if t could be found as a function of z,y,z,% ,y ,z , and H, it is 
obvious that its partial differential coefficients with respect to these quantities 
would give the motion completely. 

But, neglecting altogether the initial limit, we see that 

/dr\ 2 /(?t\ 2 /-^t\ 2 _ 1 f/dx\ 2 /<%\ 2 , (dz > \\ 
\dlc) + \dy) + \fa) ~ v* \\dt) + \dt) + \dt) ) 

1 1 

~y 2 ~2(H-V) • ' • ( 2 )- 

6. It can be easily shown, by a process similar to that employed for Varying 
Action* that, if any integral of this equation can be found, its partial differential 
coefficients with respect to x, y, z are respectively equal to the corresponding 
components of the velocity, in a curve which is a brachistochrone for the given 
forces, each divided by the square of the whole velocity. 

A complete integral of (2) must of course contain, besides H, two arbitrary con- 
stants a, (3. If, then, t be a complete integral, the equations of the brachisto- 
chrone are easily shown to be 

^= a - U=» (3); 

where & and 3$ are two new arbitrary constants. 
Also we have the relation 



dr 

dR 



/'dt Cds //4 v 



7. Before proceeding farther with the theory, we may apply the results 
already obtained to one or two well-known problems ; commencing with the 
original case proposed by Bernoulli. 

8. To find the brachistochrone, when gravity is the only impressed force, and the 
particle has the velocity due to a fall from a given horizontal plane. 

Taking the axis of y vertically downwards, we have 

V= - gy. 
Also, we may write 

K = ga. 

* Thomson and Tait's Natural Philosophy, § 323, or Tait and Steele's Dynamics of a 
Particle (2d edition), §§ 252, 253. 



150 PROFESSOR TAIT ON THE APPLICATION OF HAMILTON'S 

Hence 

(d,T\ 2 /^ T V f^ r \ — ^ 

doc) + \dy) + \dz) ~ 2g(a + yy 

This equation is obviously satisfied by 

/dr\ doe 

\^2/ (ft 

Hence -^= ™ that is the path is in a vertical plane. We may take this as the 
plane of xy. Hence our equation becomes 

sdry + (dr.\ 2 .= 1 . 

Vote/ \dyJ 2g(a + y) 

We may now write 



dT _■ 1 

dx \/2gb 

\dy t 2g\a + y bJ, 



(5). 



where b is an arbitrary constant. 
By (5) we have, at once, 



V2(f r = -£ + fay J— 1 

Hence the equation of the brachistochrone is (by § 6) 



(6). 



dr 

— = const. 

db 



or C 

' a + y b 



- _ £L J_ 1 / * ^ 

6t + 6 2 7 r~r~ _ r ' 

that is, changing the constant, and effecting the integration, 

°i = - * -n/(» ~ ^) (« + 2/) + | vers^ ?£ + ») (7 ). 

the common equation of the Cycloid, the velocity at any point being that due to 
a fall from the base. 

In this case we have evidently 



CHARACTERISTIC FUNCTION TO SPECIAL CASES OF CONSTRAINT. 151 

dr _ _ fds_ _ 1 dr 1_ f dy 

dR J v s ~ g da~ ' W2g*J (a + )2 / 1 _1 

*" a + y b 



2g**a + y 6 "*" a 



~ s/2g 
The above (at first sight apparently too limited) assumptions 

dx ' dz ' 

and the consequent reduction of the question to a plane problem, may seem to 
require some justification. This is easily supplied, thus : In the equation 



\dx) + \dy) + \dz) ~ F2 ' 



the direction-cosines of the tangent to the brachistochrone, at the point as, y, z, 
are, by (1.), 

,_ ldT 1 dT _ 1 dr 

l -¥dx^' m ~F%' n ~Fdz' 

At the adjacent point z + 8x,y + 8y,z + 8z, where we have, of course, 



the value of I becomes 



8x 8y 8z ?> 
-j- = -* = — = be, 
I m n 



dr . d 2 r 5, d 2 r 5> d 2 r 



r _ dx dx 2 ' dxdy " dxdz 
F + SF "~ 

dr 8s (dr d 2 T dr d 2 T dr d 2 r \ 
_dx F \dx dx 2 dy dxdy dz dxdz J 

F + 8F " 



8s 



dr /d¥\ 
_ dx \dxj 

~ F + 8F ' 

But in the above problem F is a function of y only, and we must therefore 

have 

V_ = l 

n' n ' 

which shows that the curve is in a plane parallel to the axis of y. 

9. To find the Brachistochrone when the force is central, and proportional 
to a power of the distance; the velocity being also proportional to a power of the 
distance, that is, being the velocity from infinity if the force is attractive, from the 
centre if it is repulsive. 

VOL. XXIV. PART I. 2 T 



152 PROFESSOR TAIT ON THE APPLICATION OF HAMILTON'S 

and the central force at distance r is evidently 

dV _ nfi 
~ ~dr~ ~ 2r n + l ' 

Thus (2) becomes 

f^lY + (*L\ 2 + f^X - - 

\dx) \dy J \dz) "~ fx 
or, changing to polar co-ordinates, 

\dr) + r 2 \dd) + r- 2 sin 2 \tf0/ 

It is obvious that we must take 



dr\ 2 r" 



^=0 

d<p ' 

which shows that the path is in a plane passing through the centre of force. 
The above equation will then be satisfied by 

dT - n — — P" " r 
dd~ ' dr~sl^-^r- 

Hence we have 



=««+/*-JF?' 



■=«»+^{^- 1 - coI, ^} +c - 

And the equation of the brachistochrone, which is evidently a plane curve, is 

2a 



I_J A*"* ■ ^ J; 

V W" 1 r * r"+ 2 



2 -i V/JLCL 

= — pr cos " + 2 : 

« +2 r 2 

!L±2 /- n+2 .. _, 

or r 2 = -v/^a sec — ^ — (#-&), 



CHARACTERISTIC FUNCTION TO SPECIAL CASES OF CONSTRAINT, 
while the equation of the free path is 

r r \ n-2 n _2 



/r\t=l n-2 , a , n. 



The above integration fails in the case of n = —2 ; that is, when the force is 
repulsive and directly as the distance, the velocity vanishing at the centre of 
force. But in this case 



t = ad + J- - a 2 log Or, 
r 



and the equation of the brachistochrone is 

a 



«=0- /J~~ 2 logCr, 

^ fJL a 

the logarithmic spiral. Eliminating r between these equations, we see that the 
time is proportional to the polar angle. 

Since a definite form has been assigned to the expression for the velocity in 

dr 

this problem, it is obvious that H is given, and therefore that there is no -r^- 

The assumption 

^ = 
d(p 

is easily justified, in the case of any equation of the form 

^Y-uiY^Y-L * f dT Y--F2 

\dr) + r 2 \dd) + r 2 sin 2 6 \d<[>) ~ ' 

if F be a function of r only. For 

o,/cZt\ d 2 r «, d' 2 r * n d 2 r «, 

8 W) = drift 8r + ddd4> 86 + W 8 * ■ 
But 

dr _ ™ dr dr _ -^ 2 rdd dr _ 2 r smdd(p 

dr ~~ dt ' rdd ~ dt ' r sinBdcf) ~ dt 

Hence 

* /dr\ _ 8t_ jdr_ d 2 T 1_ dr d 2 r 1 (fr (Pt\ _ St fd¥\ 

\d(p) ~ F 2 \dr drdcf) r 2 d6 dddQ + r 2 sin 2 d d(p d^jF V#j ~ 

dr 

That is, unless F contains <p, t-t is necessarily a constant, (3 suppose. 

But, in the present case, if we give this constant any value but zero, we intro- 
duce a problem much more general than that proposed, for the expression for the 
reciprocal of the square of the velocity becomes 

r!_ ft 2 

fj. r 2 sin 2 <9 ' 



154 PROFESSOR TAIT ON THE APPLICATION OF HAMILTON'S 

10. As an example of a tortuous curve we take the following : 
Determine the form of the brachistochrone when the velocity at any 'point of 
space is proportional to the distance from a given line. 

Taking the line as the axis of z, our equation obviously becomes 



\dx) + \dy) + \dz) - x* + 



*rtf 
Hence 

dr 



dz~ a > 



and, substituting this, and changing to polar co-ordinates in a plane parallel to 
xy, 

\dr) + r 2 \dd) ~ r*~ a ' 

Hence we may take 



dd~ p ' 



and there remains 



Integrating, we have 

r = az + 3d- Vtf^p* log. \ y^^ + J'^fi- - a 2 ] + \/a a -^-oV . 

By equating to constants the partial differential coefficients of t with respect to 
a and (3, we obtain the two equations of the brachistochrone 

en ar ' Z 

%L = Z — 



y/a 2 - fi 2 + Va 2 -B 2 - a 2 r 2 ' 

The former of these is the equation of a sphere, as may be seen at once by 
putting it in the form 

a (z-®) = Ja 2 ^- J a 2 -B 2 -a 2 r 2 . 
The remaining equation, by altering the value of 13, may be reduced to the form 






a 2 -B 2 ( 
a 



2 vg -P=rU ' ' + € 



which is at once recognised as a cylinder, whose base is one of Cotes' Spirals. 
Also, if we remark that, by (1), 

ctf_ , dr _ r 2 §__§v 
dt rdd ~~ a 2 r ~ a 



CHARACTERISTIC FUNCTION TO SPECIAL CASES OF CONSTRAINT. 155 

we see that 

d6 

. r dt (3 

cos -A = ■ = '— = const. 

v a 

where 4. is the inclination of the element rSd to the corresponding element 8s of 
the brachistochrone. That is, the brachistochrone cuts all circles on the above 
sphere, whose planes are parallel to xy, at a constant angle. {Loxodrome.) 

11. It is easily seen that 

T = C 

is the equation of an Isochronous surface. 
Also, since 

fdr\ fdr\ fdr\ 

\dx J \dy / \dz ) 

dx dy dz 

dt dt dt 

the brachistochrone cuts all such surfaces at right angles. 

And the normal distance between two consecutive isochronous surfaces is 
proportional to the velocity in the brachistochrone of which it forms an element. 
For, of course, 

8s=VOT. 

12. Generally, putting 

_ /dr\ 2 /dr\ 2 /dr\ 2 1 

* = (dx) + (dy) + U) = 2(H=T) ' (7). 

1 



(8), 



we have 



and x _ 

with similar expressions for Y and Z. 
Also, by (1), we have 



2(H- 


V): 


_ ® ' 




\dso . 


) = 


1 

2W 


d® 
dx 











dT _ 
dx 


UX ,, \ 


and 








dT 

dE ~ ' 


- r®dt j 


Hence 






d 2 x 
dt 2 


_d n dT\ 

~ dt\®dx) 

__ 1 d /dr\ 
~Wdt \dx) 


1 dTdM> 
® 2 dx dt * 


VOL. 


xxrv. 


PART I 









(9), 



(10). 



2u 



156 PROFESSOR TAIT ON THE APPLICATION OF HAMILTON'S 

But d (dr \ _ <Pt dx d 2 T dy d 2 r dz 

dt\dx) ~ dx 1 dt dydx dt dzdx dt 

_^^d^d^ d 2 r dr d^dr\ J^ dM 
~®{dx 2 dx + dydx dy + dzdxdz ) " 2® dx ' ™'' 

which is the ordinary form of the equation of the brachistochrone, (A) in § 4. 

Also, dM _ 2 f dT d Sdr\ drd_ /dr\ dr d /dr\ \ 

dt ~ \dx dt \dx) dy dt \dy) + dz dt \dz) f 

IT dr_<ffl , dj^M dr <ffl) 
~W\dxdx + dy~dy + dzdz) ( 12 )" 

d 2 x 

The above value of -r^ becomes therefore 

dr 
<Px _ J^ d& _ jr- f dr d® dr_ m dr ffl, \ 

dt 2 ~ 2W dx — \dxdz + dydy + dzdz$ ' ' ' (13) ' 
which (8) reduces to the form 

dr 
d 2 x v , n -;— ( „ dr ^ T dr „ dr ) 

aT = -X + 2*{x s - + Y^ + Z^-} . . (14). 

And we have, of course, similar expressions for -J[ and -A-. 

13. We may thus easily prove the fundamental property of brachistochrones 
given in most treatises on dynamics. 

The pressure on the curve, due to the motion, is equal to that due to the impressed 
forces. 

For (14) may be written 

ff = -X + 2^®{x^+Y^ + Z^l 
dt 2 dt \ dt dt dt \ 

— _X + 2— JX— + Y^-+ Z — ^ 
ds \ ds ds ds J 

=X-2JX- — (X — + Y^-+ Z — \ l- 
\ ds \ ds ds ds J J 

Now X ;^-+ Y 77^+ Z ;r" * s tne component of the impressed forces along ds. 

Hence 

v dx / v dx v dy „ dz\ 

Y_^(X^ + Y^+Z^V Z-^(X^+Y^ + Z^V 

ds \ ds ds ds J ds \ ds ds ds / 



CHARACTERISTIC FUNCTION TO SPECIAL CASES OF CONSTRAINT. 157 

are the rectangular components of the component of the impressed force per- 
pendicular to the path. 

But, if R be the force of constraint, X, /jl, v, its direction-cosines, we have by 
ordinary kinetics 

d 2 x 



- X - RX, &c. 



Hence KX=2 (x - * (x| + t| + Z *)) , to, to, 

and therefore the whole pressure is double that due to the impressed forces. 

From the above follows also the well-known theorem, that the osculating plane 
of the brachistochrone contains, at each point, the resultant of the impressed forces. 
For it has been shown that this resultant coincides in direction with the centri- 
fugal force, and the latter of course lies in the osculating plane. 

14. Another, and perhaps simpler proof of the theorem above is furnished 
directly by (10). Thus, squaring and adding the three equations of that form, 
after substituting in them from (11), we have 

(&x\ /AY , fdh\ 2 _ i u<m\ 2 fd®y (<mv 
\w) + \dt 2 ) + \dty ~ ±w \\dxj + \d y ) + \&J 



1 d& (dr dM fad® ,dr_d&\ 
®* dt \ dx dx dy dy dz dz ) 



+ ®* \dt) \\dx) + \dy) + \dz) S 
- 1 $( M W ( M W ( M \*\ l m (® d ®\4- 1 ( M \ 2 (fh 

= 4p tw + \dy) + v&y i " w dt (® -dirw \di) {W) 

[ by (12) and (7) ] 

I ( /d®\ 2 /d®\ 2 /d®\ 2 ) , , v 

= ip { Km) + Kdy) + (& ) } = X2 + Y2 + Z2 > b y (8). 

Hence the whole acceleration is equal to the resultant of the impressed forces ; and 
therefore the component of the acceleration, normal to the curve, must be equal 
to that of the resultant of the impressed forces ; from which the theorem follows 
at once if we can show independently that the resultant of the impressed forces 
lies in the osculating plane. This is easily done as follows. We have 

*•=?$*•*■ b y( 9 >- 

Hence "*-£«(£)- $«* * 



158 PROFESSOR TAIT ON THE APPLICATION OF HAMILTON'S 

Now, by (8) and (11), 8(~? j &c, are proportional to the direction-cosines of the 

resultant force, which therefore lies in the common plane of two consecutive 
elements of the curve. 

15. The equation of the surfaces which are orthogonal to the path is 

r=C; 

and that of equipotential surfaces 

V=C 1 . 

That these may coincide we must have 

T = 0(V), 

where <p is any function whatever. 
Hence 

/^rml 2 (f dY \\ f dY \ 2 ■ f dY \ 2 \ 1 

|^ (V) } \\dx) + W) "(^)> 2(H-V)- 

If we write 

V =Jj 2 (H - V) cp' (V) dV = * (V) , . . (15). 

this becomes 

m+QHT)'^- ■ ■ ■ ■ < 16) - 

A complete primitive of this equation is, of course, 

V = Ix + my + nz — p , 
where p is any function of I, m, n, and 

V- + m 2 + n 2 = 1. 

The general primitive, equated to a constant, is therefore obviously the equation 
of a series of surfaces such that the normal distance between any two consecutive 
members of the series is everywhere the same. It is evident from (15) that the 
surfaces thus found are identical with the isochronous and equipotential surfaces, 
when these coincide. The equations of their orthogonal trajectory, that is, of the 
free path which is also a brachistochrone, are therefore, 

( d E\ § (<®!\ § (^E) s 

8x 8y Sz \dx) " \dy ) ^ \dzj 



= 3F = 8C, (17). 

tej \dy) Vfa) \dx) + \dy) + \dz ) 

Hence, 



t<ffi 

\dx 



*.=*>(£[).*»■. 



CHARACTERISTIC FUNCTION TO SPECIAL CASES OF CONSTRAINT. 159 

and, therefore, 

*-*{(S)>+(S)v(S)*} *«>(©• 

But, substituting the values of das, &c., from (17), this becomes 

* - W { (f)(5) + OiSk) + (S)GS) } + *° (f) • 

and the first part vanishes, by (16). 
Hence 

frx _ fry = 8*z = 8 2 Q 
dec Sy dz §C 

which show that when the path is simultaneously a free path and a brachisto- 
chrone, it is necessarily rectilinear. 

This might have been inferred at once, from the theorem of § 13, which shows 
that if the free path be a brachistochrone, there can be no pressure due to the 
motion, i.e., no curvature. But the above investigation is given as containing 
curious additional information. It shows, for instance, that if the force be the 
same at all points of each of a series of equipotential surfaces, the lines of force 
are rectilinear. Also, that if the flux of heat be constant per unit of area over 
each one of a series of isothermal surfaces, though not necessarily the same for 
all, the propagation of heat takes place in straight lines. And, as particular cases 
of these theorems, if the force or the flux of heat be the same throughout a given 
space, the attraction, or the flux, therein takes place in parallel lines. 

16. Hamilton's equation for the determination of the Characteristic Function 
(A) in the case of the free motion of a single particle is 



@y+®y+@y-*-y>. . . . m 



The comparison of this with (2) suggests a useful transformation. Introducing 
in that equation a factor 2 , an undetermined function of z, y, z, we have 

■ 2 ' idr\* & 



If we make 
and 

(19) becomes 



6 = <t>'(r) . . . . . . (20), 

6* 



2(H- V) 



= 2(1^-^) . . . . (21), 



(^HiFM^y^-v,). . . m 

VOL. XXIV. PART I. 2 X 



100 PROFESSOR TAIT ON THE APPLICATION OF HAMILTON S 

Here it is obvious, by (18), that (t) is the action in a. free path coinciding with 
the brachistochrone, and that 2(H X — Y x ) is the square of the velocity in this path. 
Hence the curious result that, if r be the time through any arc of a given 
brachistochrone, the same path mill be described freely under the action of forces 
whose potential is V a , where 

2(Hl ~ Vl) = 2(H - V)' 

0' being any function whatever ; and (p(r) representing the action in the free path. 

17. The simplest supposition we can make is that </>'(t) is constant. In this 
case the velocity in the free path is inversely proportional to that in the brachis- 
tochrone at the same point ; and the action in the one is proportional to the 
time in the other. In fact, as Professor W. Thomson has pointed out to me, in 
this case the investigation may be made with extreme simplicity, thus — 

In the brachistochrone we have 



/ 



ds . . 

— a minimum. 

V 



Putting v = - , and considering v as the velocity in the same path due to another 
(easily determinable) potential ; we must have 



/■ 



vds a minimum. 



This is the ordinary condition of Least Action, and belongs, therefore, to a free 
path. 

Hence, since the cycloid is the brachistochrone for gravity, and since in it 

v 2 = 2gy, it will be a free path if v 2 = „ — , that is for a system of force where 

the potential is found from 

H — V — — 

1 l ~*w 

This gives 



da; dy fyy 

In other words, a cycloid may be described freely under the action of a force 
towards, and inversely as the square of the distance from, the base; and the 
velocity at any point will be the reciprocal of that in the same cycloid when it is 
the common brachistochrone. 

This result is easily verified by a direct process. 

18. But we have, by § 16, an infinite number of other systems of forces under 
which this cycloid will be described freely. 



CHARACTERISTIC FUNCTION TO SPECIAL CASES OF CONSTRAINT. 161 
For by § 8 we have, putting a = 0, since the base is now the axis of x, 

= JL _ J b C0 "sV| + Jl Vb=y~+ C. 
Hence, whatever be <p', the cycloid is a free path for the system 

\<t>' (^ b - jtcoiJi+^Vb^+c)]* 

v > = 2^-v t ) = ^-^ Wy L-. 

19. The converse of the proposition in § 16 is also curious. Taking Hamil- 
ton's equation (18), we have, 



(0'(A)y{(0 + (fy + (f) a }= 2 (H-v)(« A ))» 



• (23). 



Comparing this with (2), we see that t = <p (A) is the brachistochronic expres- 
sion for the time in a path which is a free path for potential V. The requisite 
potential is now found from 

^- ir ,=2(H-V)(^(A)) 2 ... . (24). 



2(H X - VJ 



Hence, if A be the action in a given free path, the same path mill be a brachis- 
tochrone for forces whose potential is V x , determined by (24), V being the potential 
in the free path. 

Thus, the parabola 

(,v — &) 2 = 4a (y — a) 

is the free path for v i =2gy. And the action is given by 

1 2 1 

A = xja + ~( y - a y. 



V2g v 3 

Hence this parabola is the brachistochrone for 

1 



2(H 1 -V 1 ) = 



2Mtf>'(A)) 2 
In the simplest case (p'(A) = 1, and we have 

_dy 1 _ _^Yi_ L 

cfcc ~ ' dy ~ kgy 2 ' 

Hence, by § 17, the parabola is a brachistochrone when a cycloid is the free path. 
20. Again, if 

* 2 = 2(£-h), . . . (25, 



162 PROFESSOR TA1T ON THE APPLICATION OF HAMILTON'S 

where H and fx are essentially positive, the free path is an ellipse of which the 
origin (the centre of force) is a focus. 

This ellipse is the brachistochrone for the potential V 1 , and whole energy II l , 
where 

2(H 1 -V 1 ) = 2 (r -11 )' 



or 



This corresponds to a central force 



2 

Or 

4(//-Hr)' 



dV 1 _ _C CHr 

dr - 4(/z-Hr) + 4(/x-Hr) 2 



_C^ 

~ 4(/x-Hr) 2 



The velocity at any point is 



/ Cr 

V '2(lL - 



2(/x-Hr)' 
In the ellipse, we know by ordinary kinetics that 

Comparing this with the above formula (25) we have 

Hence the velocity in the free ellipse is 

v=j£j?^' ■ • ( 26 > 

x a ^ r 

That in the same ellipse, when it is a brachistochrone, is, as above, 



/ Cr jQa I r 



2(/z-Hr) ^ fx * 2a 

But if we refer it to the other focus of the ellipse we have 

r x = 2a — r . 

Hence 

Comparing (26) and (27), we have the singular result that a planet moving 
freely about a centre of force in the focus of its elliptic orbit is describing a brachis- 
tochrone {for the same law of velocity as regards position) about the other focus. 
The reason of this remarkable property, as well as of the connected one that 



CHARACTERISTIC FUNCTION TO SPECIAL CASES OF CONSTRAINT. 163 

while the time in an elliptic orbit is {of course) measured by the area described 
about one focus, the action is measured by that described about the other* is easily 
traced to the fact that the rectangle under the perpendiculars from the foci on 
any tangent is constant. 

21. It follows from Hamilton's investigations, that in the free ellipse we 
have 

2 (£ - H) dr 



h 



x/ 2 (^-H)--f 
\r ) ir 

where a depends upon the excentricity of the ellipse by the formula 



2H 



- ft* a 



The theorem may therefore be generalized as follows : — The free ellipse will be a 
brachistochrone, if the velocity be given by 

1 



«« = 2(H 1 -V 1 ) = 



2(£-H) |0'(A)} 2 



where <p' is any function, and A is the integral last written. By differentiation 
with respect to r, we get the law of central force requisite. 

But results of this nature may be deduced to any desired extent, without more 
trouble than the requisite integrations involve. 

22. The examples immediately preceding are but particular cases of the follow- 
ing general theorem, which is easily seen to be involved in the results of §§ 16, 19. 
If we have two curves, P and Q, of which P is a free path, and Q a brachis- 
tochrone, for a given conservative system of forces ; P mill be a: brachistochrone 
for a system of forces for which Q is a free path — and the action and time in any 
arc of either, when it is described freely, are functions of the time and action 
respectively, in the same arc, when it is a brachistochrone. 

23. It is easy to see, that there exists a very singular analogy between the 
processes we have just given, and those suggested by certain problems in optics. 

Assuming, for an instant, the exploded corpuscular theory of Light, Varying 
Action is at once applicable to the determination of the path of a corpuscle. On 
the other hand, if we assume, as our fundamental hypothesis, that light takes 
the least possible time to pass from one point of its path to another, the foregoing 
investigations would be directly applicable to find the path in a medium whose 
refractive index (on which the velocity depends), at any point, is a given function 
of the co-ordinates ; in other words, in a heterogeneous singly refracting medium. 

In the beautiful investigations of Hamilton, on the Theory of Systems of Rays 

* Proc. R.S.E. March 1865, or Tait and Steele's Dynamics of a Particle (2d edition) § 258. 
VOL. XXIV. PART I. 2 Y 



164 PROFESSOR TAIT ON THE APPLICATION OF HAMILTON'S 

(Trans. R.I.A., 1824-32), the path of a ray is assumed to be a straight line in 
any one medium. Here the velocity depends only upon the direction of the ray, 
as in homogeneous doubly refracting media, and the problem has no analogy with 
the conservative case which is treated above. 

24. As an instance of an optical problem I take the following, due I believe to 
Maxwell* If the refractive index of a medium be such a function of the distance 
from a given point that the path of any one ray is a circle, the path of every other 
ray is a circle ; and. all rays diverging from any one point converge accurately in 
another. Or, in another form, find the relation between the velocity and the 
distance from the centre of force that the brachistochrone may always be a circle. 

The symmetry shows that our investigations need only involve two dimensions. 
Taking the centre of force as pole, the equation of a circle is 

r 2 - 2ar cos (6 - &) = f - a 2 , = b 2 suppose. 

Hence 

a = 6 — cos — ^ . 

2ar 

This is obviously the equation before written (3) in the form 

dr 

Hence 



a. 

da ** 



= a6-Jd 



da cos 



2av 



But, if v be the velocity (the reciprocal of the refractive index in the optical 
problem), 

/dr\ 2 _l_/rfr\ 2 -l 
\dr) + r 2 \dd) ~ V 2 ' 

Hence 

dT JT a 2 d f\ ^ b 2 -r 2 C b 2 + r 2 

dr~ W v 2 ~ r 2 _ drj da °° S 2ar ~ ~J da r J(4a 2 r 2 - (6 2 -r 2 ) 2 ) ' 

But v is not a function of a, so that we get by differentiation with respect to 
that quantity 

a 

r 2 b 2 + r 2 ■ 

J\ _ a 2 ~ r V(4a 2 r 2 - (6 2 -r 2 ) 2 ) ' 

This is easily reduced to 

(b 2 + r 2 ) 2 _ (b* + r 2 ) 2 
~i(a 2 + b 2 ) - 4p 2 ' 

The condition, that v is a function of r and absolute constants only, thus leads 

* Cambridge and Dublin Math. Journal, IX., p. 9. 



CHAKACTERISTIC FUNCTION TO SPECIAL CASES OF CONSTRAINT. 165 

at once to two conclusions : b is an absolute constant ; and so is 2ga, for which 
we may write c. a is therefore inversely as the diameter of the circle ; and 



-,2 



+ r 2 



From the form of the equation of the path it is obvious that — b 2 is the 
rectangle under the segments of any chord drawn through the centre of force. 

Hence, in the optical problem, if a ray leave, in any direction, a point distant 

r from the origin, it will pass through another point in the prolongation of r, 

b 2 
distant — from the origin ; and, in the kinetic problem, there is an infinite number 

of brachistochrones (circles all, and the time being the same for all) when two 
points thus related are taken as the initial and final points. 

25. Such examples might be multiplied indefinitely. For instance, if the 
refractive index of a medium be inversely proportional to the square root of the 
distance from a given point, the path is a parabola about the point as focus ; 
that every ray may be a cardioid whose cusp is at the point, the square of the 
refractive index must be inversely as the cube of the distance : and so on. 

26. The processes of § 4 may of course be applied to innumerable problems 
besides the determination of the form and properties of brachistochrones, but I 
shall content myself with an example or two. Thus, if we take 

as the characteristic function, we have 

d<P f( v ) dx . , dO r 

d^= vdt> &c -' and m=Jf^ dt 

Of this, besides the cases f(y) — v, and /(#) = -, which we have already con- 
sidered, the most curious is that where 

V 2 

/M = |; 
that is, when the space average of the kinetic energy is a minimum. In this case. 
/<20\ 2 (d&\ 2 (d&\ v * 

, d<£> 

and -tj = s. 

dH 

Again, if we take 



O =J*F(x,y,z)f(v)ds 

d$> -Ffdxn A d<& r 

-dx-=vdt> &C -^ n<i dll=J F SM dt 



166 PROFESSOR TAIT ON HAMILTON'S CHARACTERISTIC FUNCTION, ETC. 

TT .„ -n / \ Constant 

Hence, if F (a>, y, z) = . . ■ , 

we have -= = Ct, 

so that there is an infinite number of values of the characteristic function, besides 
that of Hamilton, which give the time through any arc of the orbit by their dif- 
ferential coefficients with respect to H. 

27. Enough of this ; I conclude with the remark that various investigations 
in Statics supply us with excellent examples in our subject.* Take the common 
catenary, for instance, its equation is found by the conditions 

I yds = minimum, and I ds = constant, 

the axis of y being directed vertically upwards. 
This gives 

Sf(y + a)ds = 0. 

Hence the catenary is the free path of a particle whose velocity is given by 

v = G (y + a) ; 

that is, if the force be in the direction of, and proportional to, the ordinate, and 
repulsive from the axis of x. In the same way we see that the catenary is the 
brachistochrone if the velocity be inversely as the distance from the axis ; that 
is, if the force be attractive, and inversely as the cube of the distance from the 
axis. 

* Compare Thomson and Tait's Natural Philosophy, §§ 581, 582. 



( 167 ) 



XIV.— On the Tertiary Coals of New Zealand. By W. Lauder Lindsay, M.D., 
F.L.S., &c, Honorary Fellow of the Philosophical Institute of Canterbury, 
New Zealand. 

(Read 20tli February 1865.) 

Coal deposits of Tertiary age have now been found more or less throughout the 
two great islands (north and south) of New Zealand. They are best known, and 
they have been chiefly worked, however, in the provinces of Otago, Nelson, Canter- 
bury, and Auckland. Their apparent more meagre development in other provinces 
is probably simply due to the circumstance that the latter have not, as yet, been so 
thoroughly explored or so extensively colonised and peopled as the others. The 
explorations, however, of provincial and geological surveyors, of prospecting gold- 
miners and sheep-owners, and of other pioneers of civilisation, are daily adding to 
the number of the known coal-fields of New Zealand ; and it is probably not going 
too far to assert, in general terms, that the whole area of its two great islands is 
studded over with coal-basins of various extent, depth, age, and quality of coal. 

In Otago the following are the districts which possess coal-fields or basins of 
Tertiary age : — 

1. District between Dunedin (the capital) and the Taeri plains ; including 

especially what I may designate the Saddlehill or Greenisland Basin ; 
and the Silverstream valley. 

2. Tokomairiro valley; a. Upper (Woolshed), and b. Lower (Tokomairiro 

gorge). 

3. Great valley of the Clutha river — 

a. Upper (Dunstan, Kawarau, and Manuherikia districts ; Cromwell, 

Clyde, and Alexandra townships). 

b. Middle (Teviot, Tuapeka, and Waitahuna districts ; Laurence and 

Wetherstone's townships). 

c. Lower (Kaitangata and Coal Point). 

4. Valley of the Upper Taeri and Shag river — 

a. Upper (Mount Ida or Highlay district). 

b. Lower (Shag or Vulcan Point). 

5. Valleys or beds of the Waitaki and Waikawa rivers ; Otepopo &c. ; 

all mostly in the central and eastern districts. 

These localities include, fortunately for the gold-mining interest, the great 
gold-fields of Tuapeka, Dunstan, and Mount Ida or Highlay ; and, as a general 

VOL. XXIV. PART I. 2 Z 



168 DR LAUDER LINDSAY ON THE 

rule, there are few of the gold-fields destitute of local deposits of Tertiary or 
brown coals. The discovery and rapid development of the rich and extensive 
gold-fields of Otago are the main causes why in this province the coals in question 
have been more largely worked than in any other part of New Zealand. * 

Throughout the province of Canterbury similar coal-deposits occur, and more 
especially in— 

1. The valleys or beds of the Selwyn, Upper Waikamariri, Rakaia, Rangitata, 

Ashburton, Northern Hinds, Potts, Tenawai, and other rivers. 

2. The Malvern Hills, Mount Somers, Big Ben Range, Thirteen Mile Bush, &c. ; 
all mostly in the central or eastern districts. 

In the province of Nelson, Tertiary coal-deposits stretch along the— 

1. West coast, from Cape Farewell with little interruption to the Grey river 

on the Canterbury boundary line — overlying unconformably the secon- 
dary Coal-measures of the Buller and Grey rivers. 

2. On the northern and north-western coasts, they occur at Motupipi in Massacre 

Bay ;Ennerglyn, near the town of Nelson, &c. 
In the province of Auckland they stretch along the — 

1. West coast with little interruption from Kawhia to Hokianga (including 

Aotea, Raglan, Manukau, and Kaipara). 

2. On the east coast they show themselves at Mongonui in the north, and 

further south at Wangeroa and Matakana, &c. 

3. In the interior they abound in the Upper and Lower Waikato ; Waipa ; and 

Drury (or Hunua) districts. 

Towards the close of 1861 I lived for three months in the centre of the 
Saddlehill Coal Basin in the immediate vicinity of Dunedin. Within a couple of 
miles of my residence (ten miles from Dunedin) an excellent artificial section of 
the brown coal strata was exposed in the Saddlehill Colliery, on the flank of the 
conical basaltic mass of Saddlehill (height 1565 feet). There is here a regular 
adit of considerable length, with relative tramways and other works. This 
colliery had been in successful, though limited, operation for several years ; but 
at the period of my visit the superior attractiveness of the recently discovered gold 
field of Tuapeka had absorbed all available labour, and the works were conse- 
quently temporarily stopped. A semi-artificial section I also found in the imme- 
diate neighbourhood of my headquarters (the farm-house of Fairfield^ — viz., in 
Abbott's Creek, where brown coal had also been worked for a very short time, 
and on a very limited scale. Natural outcrops or sections of similar strata I 

* In all probability it •will yet be found that the Tertiary coals of New Zealand are referrible 
to groups of three distinct ages, — corresponding so far to our Eocene, Miocene, and Pliocene subdivi- 
sions. Dr Hector already regards the Otago brown coals as of three distinct ages, and Dr Haast those 
of Canterbury as of at least two. Those which are mined as fuel are — for the most part at least — 
apparently referrible to the older or lower groups, or subdivisions, of the New Zealand Tertiaries. 



TERTIARY COALS OF NEW ZEALAND. 169 

found on Scrogg's Hill — a continuation southwards of Saddlehill — where they were 
included in a Government coal-reserve ; in M'Coll's Creek, on the seaward base of 
Saddlehill ; and at other points on the flanks or base of this basaltic nucleus. 
I was led, while on the spot, to the conclusion that the Trappean mass of Saddle- 
hill, with adjacent minor eruptive Trappean masses, had burst through what had 
at one time been a continuous coal-bed or basin subsequent to the deposition of 
the latter ; or, in other words, in newer Tertiary times. That the coal-bed in 
question is more or less continuous is so far proved by the fact, that since I left 
Otago no less than three large collieries have been established in the immediate 
vicinity of my former residence. The first of these — the Fairfield Colliery — was 
opened on the lands of Fairfield itself, very near the old workings of Abbott's 
Creek, which I frequently examined. The proprietor, my friend Mr Martin, late 
Member of the Provincial Council of Otago, tells me* there are here two main 
seams, the upper six and the lower four feet thick, with a " dirt-bed" between 
them. The other pits, all within a few hundred yards of each other, are the Shand 
and the Walton Park Collieries. The strata associated with the brown coal are 
mostly various shales ; clays, bituminous, and arenaceous, some of them plastic, 
white, and micaceous ; and sands or sandstones of various degrees of coarseness. 
The whole are overlaid by the newer Tertiaries so abundant in the district, con- 
sisting of variously coloured clays, sands, and conglomerates. 

Daily pedestrian excursions during my residence in the Saddlehill district 
gave me frequent opportunities of studying all the natural and artificial sections 
of the brown coal strata of this basin, and of collecting hand-specimens of every 
quality of the coals so exposed. The latter were brought home, and a suite 
thereof submitted in 1862 to careful chemical analysis by Professor Murray 
Thomson, a Fellow of this Society, then an analytical chemist in Edinburgh, and 
now Professor of Experimental Science in the Thomason College, Roorkee, 
Bengal. The results of his analysis are embodied in Table II., and fully bear out 
the opinions to which, when in Otago, f I gave public expression, regarding the 
economical value of the Otago brown coals. 

While in Otago I also visited the Kaitangata coal-field at the mouth of the 
Clutha, about 60 miles southward of Dunedin. Here there are works which were 
originated, and are now carried on, under the patronage of the Otago govern- 
ment. There are not only regular adits at the pit ; but the pit is connected by 
means of a rail or tramway two miles in length, with a jetty on the Clutha 



* Letters of January 1862 and September 1863. 

f In a lecture on " The Place and Power of Natural History in Colonisation-, with special 
reference to Otago (New Zealand)," prepared for and printed by the " Young Men's Christian 
Association of Dunedin," Dunedin, January 1862. Extracts therefrom reprinted in the "Edin- 
burgh New Philosophical Journal" for April and July 1863. 

Vide chapter on the " Geology of the Otago Lignites." 



170 DR LAUDER LINDSAY ON THE 

for the ready delivery of the fuel into small coasting traders for the Dunedin 
market. 

At Coal Point, in the coast cliffs, two or three miles northwest of the mouth 
of the Clutha river, occur the best natural sections of the brown coal strata 
I saw in Otago. Here these strata consist of various seams of coal of different 
characters or qualities, separated by or associated with laminae or beds of con- 
glomerates, quartzose gravels, grits, and sandstones ; clays, including fire-clay, 
pipe-clay, fine coloured clays, and carbonaceous and arenaceous clays, some- 
times laminated; and carbonaceous and other shales. They contain various 
fossils, in the form chiefly of dicotyledonous leaves, fragments of lignite, stems of 
trees, and other plant impressions ; as well as ironstone concretions and iroD 
pyrites. Overlying the brown coal strata is a series of conglomerates, gravels, 
sands, and clays, generally more or less ferruginous ; of newer Tertiary age ; essen- 
tially identical with those overlying the brown coals of the Saddlehill district. 
These beds, too, contain nodules of clay ironstone, which are further scattered in 
all directions on the beach at the foot of the cliffs. Their appearance and posi- 
tion reminded me strongly of those of the carboniferous shales of Wardie. It 
does not appear that the stratigraphical relations of the Tertiary coals in other 
parts of Otago and New Zealand differ — save in minor and local details — from 
those of the brown coals of the Saddlehill and Kaitangata basins, as here roughly 
sketched. 

Before leaving Otago I visited the Tuapeka gold-field, where I had an oppor- 
tunity of seeing the relations of the brown coal, which is now being worked at 
Laurence, Wetherstone's, and Waitahuna. From Otago I passed northwards to 
the provinces of Nelson and Auckland. In neither of these, however, had I any 
opportunity of inspecting the Tertiary coal strata in situ. My examinations were 
confined to the suites of coal specimens contained in the Provincial Museums of 
these provinces, or in the hands of coal proprietors or amateur geological col- 
lectors. Unfortunately, the value of the Museum series — which, in the Auckland 
Museum at least, is somewhat extensive — is seriously detracted from by their 
careless nomenclature and classification, and by the improper or defective method 
of exhibition. The plan adopted in the Museum of Science and Art, Edinburgh, 
and in other of our own national Museums, should forthwith be copied in these, 
as well as other, colonial museums, — viz., to accompany each specimen with a 
full descriptive label, setting forth not only its locality, and date and circum- 
stances of collection, but its chemical composition ; and to classify it after some 
uniform plan, geological or chemical. Were this done, such series of specimens 
could not fail to acquire a great local as well as general value, instead of being, 
as at present, little more than a mass of lumber. 

In the Great Exhibition at London in 1862 (New Zealand department), I was 
further enabled to examine a pretty complete series of all the New Zealand coals 



TERTIARY COALS OF NEW ZEALAND. 171 

known up to that date, — especially those of the North Island, and northern por- 
tions of the South Island. Desirous of comparing the New Zealand Tertiary 
coals with local coals of greater age and superior quality, as well as with coals of 
all ages from every part of the world, I availed myself of the opportunities pre- 
sented by the Exhibition in question ; the Australian Museum, Sydney ; the 
Museum of Economic Geology and British Museum, London ; the Museums of 
Economic Botany at Kew and Edinburgh ; the Museum of Science and Art, Edin- 
burgh, and other minor museums, British or colonial. 

I have selected the Brown Coals of Otago, as representative of the Tertiary 
coals of New Zealand, for three reasons, — viz., that I am more familiar with 
them ; that they are the best known and most extensively worked in the colony ; 
and that their stratigraphical relations and chemical constitution appear essen- 
tially those of all other New Zealand tertiary coals. 

The general results of my inquiries as to the geology and chemistry of the 
Tertiary coals of New Zealand I have given in the " Abstract" [published in the 
Society's " Proceedings,"] of the paper which I had the honour of presenting to the 
Royal Society on 20th February last. The only section of the said paper which 
it seems desirable here to print in detail, is the tabular exhibition of the physical 
characters and chemical constitution of the brown coals of Otago; and as stan- 
dards of comparison of certain other or older coals of other provinces of New Zea- 
land or of Australia. 

Table I. refers exclusively to specimens collected by the Geological Survey 
of Otago, or submitted to analysis by the chemist attached to that survey* The 
majority of the Otago specimens are from the same collieries or localities from 
which my own collections were made. But inasmuch as the collections of the 
Geological Survey were made subsequently to mine, and at a period when the 
various works were in full operation, the survey specimens are likely to be of a 
quality superior to mine, which were necessarily, to a great extent, surface speci- 
mens. Moreover, the mode and scope of the analyses differ somewhat in the two 
tables ; wherefore, and on other accounts, Table I. is to be regarded as the natural 
complement of Table II. f 

Table II. refers exclusively to specimens collected by myself in Otago in the 
course of my various excursions in 1861. The chemical analyses were made, as 
before stated, by Professor Murray Thomson. 

* It is constructed chiefly from materials contained in a Report by the Government geologist of 
Otago, Dr Hector — a Fellow of this Society — of date 13th April 186i. 

•j- The natural order or sequence of these Tables has been reversed to suit the requirements of 
the printer. 

VOL. XXIV. PART I. 3 A 



£? 
m 



so; 



<-> CO 



PQ 



o 
<! 

H 

O 

Ph 

o 

o 

Q 



O 
N 
O 

o, 
i— < 

EH 

Ph 
Eh 



-I 



2 so ]3 

5- s 



,0 

a, 



ft ft 



s:s 

So 3 



-a -j 
!s>|3 



I ;1 i-S 

■ a eg 

o tf > i ~ — 

S3 ® o -a 5, 2 

Sflftlf.S 



— - 



P ft 



to 
3 



~j2 ° °5 
jq — O to 

i f -; i - 

£"3 53 Z2.S 
> 



To tl § 

■J > 






O S. 



to d 

a 



?l 



i 



£ fee' 
£■& s 



--■ *H ,-J 3J 

" u to w 
3 CO 

•43 .„ a> =S 

to u 
/ o S « 
S co -3 3 
;3 © -*jr3 

3 42 ^ 3 
- fe2 » 

•r .s « ,5 

S^g^ 

&>, „-5 
5 — .; tr. 
^ t>* set .£ 



z S s 

O 0,3 

ass 



O V 



■o o 

8 o ' 



t».S-l o 3 -5 8 



68 fe zi a _ .-§ 






3 o 



o ce =s -" -3 



"c3 ~ S" 

'S H ""■ 

- Oh 

-S— ° 

B 60S 
O *3 CP 
O '-^ e — 

ca o> 22 
8 co '3 

tS CO fl ^ 
S O O'^ 



t; s 5 to 
*= 2 .-S 

B-«»c2 



O S 2 C3 

" w ^3 .2 



• ^ T3 O o> 

cu S ^3 

^: S bo.-S 






O" PQ 



^2 
-a 



to 

3 



.-s «= 



pj 


^z 




to 


2 



OB 





Bi 














SB 


rSj 




H 


c 


cj 



6o!o 

J= S 
CO 

*■• H 

^ to 



- 



a ".a* 






co ^ e 

c >;2-s 

c- mJ* ° 

k M| a' 






53 ^ ° 



p 2 



:>? s- 






— Z ■ v t 

5 s -■« 

O 2 S § 

p; g.9 «o 

o 5 S ■- 

§■2 »"§ 

2 o fo =J 

S c) n *- 

o 
O 

CD 



"0 


> 






cS 


- 










> 




> 


s 


z 










- 






- 


rJ 



S 3 



g 

! = 
2 ? 



= w r 3 5.° = 



*> 



8^ S 

h ■- c 



2 cJ- a, | 

" i i S : 

" r C --C " 



cb ,= S 



:c 






s = — 
•2 = 7 - 

'8-3 fill 



2- 



: — -^ =: 



S a 



(D -3 4) 



a 



3 2 Pri 



-,.= >-. 



(« to K 

- - — - » 



CO rtrrt 



= 3 - - 
a"3Ss 

'12*81 



^5 
o 

-= o 
tc 

.7 ? 



g 5 



«o 



£ o j) 

S = S 

p5 2 to 



M S c 

r^ JO C3 

esc 



S O «3 c 



— ~ tc :r - 
V,2f '- 
"■ S a 



HISS 



£ 3. S 2 O 'o 



5 ^ 



a goq 

r _x 

,~ P o 

>- e^ 

mO +J-S 



C H 






0> k =3 ^- 



"1,3 

I 5 . 
< 13 

** -2 

US 

53 C3 

J— o 



;m 



o> cu ~ j; 
~ §- >^ s 

•t c_ O «> 
.- O K O 

-IJI 

C - cc C^ 

z^- 
"S -d " .- -' 

o^s— a 

nop .2 

q cJ ^ - a) 

rf°? ,-2 

a ^" l > M 

2^ 5-2 53 



Eh 

O 

Ph 

< 
O 

o 
I 

-< 
W 

& 
O 



t 



§ I 






4J g 



Q ft 



*B 




s 




rt 




02 




T* 


q 


■^ 


ft 




<r| 




-3 


on 


«2 





iz; 




w 




w 


ft 


C5 



2 >J 
S J 

2 is 

ft 



Eh 
O 

K 

X' 







"- 
o 
M 
o 

H 



3 

I 

tn 2 



tag 3 is -3 



§1 






3 13 o § 

j <>. © a> o 

«-£ o 

•-£ -.2 

2 « 0-^ 



8 3 o <3 3 



cb M _: ^ -^ & t! 

so 3 "3 is S S .2 
rt ° J= =>•£■ & 

§ SPcu^i g 



5 ..TS-sJa Pȣ5 



1> <b a 



O *a 



CB 

a s =3 

top * 

CD '^S "^ 

^ * a 

£ o= s . 

«"" ►. 

> =1 £ d 

^5 



CO 






,£3 CB ° 

I M ^ 1 

S |=g "8 

ISJ! 

«t] CO '"r^ 

w 



5 Sti-CM 



sill 



is-g-s 

<u P o> 

o *^ 

=8 S -H 
■a S"g 



O r- C3 

£ bOCD 

S-S §'-3 

H^rd g/3 

■^3,3 

^3 SI 

W -T3 a/bb 
CM 



O 

o ^ 



"3° 

> h-» 

g* 

Ph 



<B ^ CO 

cog*; 
-S-Jl-' 3 

3 « ° 

a) «OB 
W . 



C3 IB 



>> , o 

g-sa 



H 

PR 
O 
EC 



o 
o 

o 

I— I 

o 

N 

o 

Hi 
«1 



H< 



a <* 

V o 

So 



^=J 






■< 








a 


pq 


O 


EH 

o 


o 




on 




a 


^ 


fa 






o 


o 


« 


CJ 


H 


ts 


Si 


ri 


A 




u 






bll 




a 














br 


o 


-• 





o=2 

085 
~-< u o 



£ 


4S » 






^ 


<I 


n « 


o 


2p 


O 


o 




o 2 


w 

o 


"5 "B 


& 


PhW 


Ph 




CO 




1-1 












<72 


> 


w 
HP 


P5 


^ 




^ 




MM 


H 




P 




O 




m 








* 


p= 


H 


CB 


iz; 


i2| 



H 
O 
<1 

h1 
EH 
W. 
W 
<! 



G<» i— I i— I i-H 



<X) CN CO r-i r- rH 



WHCOHHCOOCOO) 



OOOlWOOlft 
ONSMOO 
CO C<l <N CC <N CO 



H^rf <U p3rJ'0)p--<D 

, H adBfi«J3sd 



g 

5 
o 




^ 
3 




(H 


Ph 


H 


Pi 




K 





|H 


3 




3 


« 


o 


a 


M 


w 


B 


H 


02 


Ph 



3 


w 


to 
o 


ft 






o 




OJ 




C3 






OJ 


^ 


S3 



02 


^ 


ti 


t> 


w 




|Zi 


CQ 


1 


a 






^ 


1 


o 


(U 


D 


Ph 



b3 






- « 


5 
S 


CH 

o 












a 


CO 


■--J 




o 






cr; 






Tl 


> 






■H 

s 

CB 

s 




e 

D 


bo fl 


03 


ci 


■in 


<?3 


a 

Fh 


»H 


CB 




Pi 










q^ 


CO 


,=; 


-= 


M 


(0 


o 
O 


CO 

cSJ 


3 
S 


ft 
> 




o 


f 

s 




r a5 






cm 

C 








CtJ 

1 




CIS 


1 


ci 


o 


f^ 


l-H 


73 


O 

O 

H 


CO 


03 

1? 


CQ 

O 

a 


cu 
> 

a; 

03 


eg 

Fh 


C 


1 














o 


CB 


c 








^1 






« 




'r-i 


O 


d 


1 

<B 


o 
S 


■a 

cd 


■2 




$$ 


S 


pC 



•jk»WBH 

•8>[00 UI 

uoq.rBf) 



O 
81!^[°A 



•93J03 UT 

uoqiEQ 



OS I-H 



fa 

ft 



O 

Cs 
< 
H 
O 

fa 

o 

w 

fa 
< 
o 
o 

t* 

03 

fa 1 

H 
05 

fa 
H 



?3 r*. Tt 



is | 

SpS 



rt a} ~ d> 



"■a «i 



eg 



111 



»3i 
■3*8 



SEN 



3^« 
o<<§ 



.s§?.| 

_.O.t3 ° 



fa o 



fa 2 6 

£~^ 

00 ;5 .9 

: || 

oil « 

«pa.a 

1 I | 

2 j S 

P ^ -P 

Is 13 

o r 1 <i> 



= is 
I g .9 ~ 

: fa §^ 
o o 



bprf 



£ S 



;gfa 

-< © 

•Sis 

'oj co 

'■*-> o 



c p 



5 2 3 

P CD 

■- o > 

T2 « 

a; i co 

Is '. J 

p B o 

'£ cH P 

5 gJ 



O fS cj 

05 <,h 

e o s 

3 ot 
O 3 



fa 






e? >- -* 

ffiOVN 

cocnco 



00 t~<M 

no cn 






rt a O 



- 'g 


of the lithol 
grai ity ; co 
«ttes, which 

lack ; compi 
gravity ; grt 
or the Meso 


eh include Brown Coals 
, including the transition 














M ,3 

rP ja 
60ti 








° § 


r^ ^" ^ ^ ^ ^ ^ 


f ^"3 
>" « o 
oT-'SD 

<u O 5 






CO ^ 


HOE ^- - =4- SJ 

^S ' ;f, O 






.2 s 
&3 


CS 5 cj - 1 C3^3 _ 

.o'S! -3 2 
H > o •- >J o o 




H 
O 


S ^ 2 -3 o " 2 

- ~ . . a ^ c s 




03 
H 

02 


3 J 


3 = s §--:~ 


» o J 






-e 


is* = ^-- ; = 

ca « c ? j --SP • 


r^o 






S3 o 
S to 
a - 


t: s o 
So - „ 


S 


p" 


O 
-ti 2 


|l| 




Jj 
■ 


p o 


> r t ^ > '. - - 


5.3-8 3 


a 






<H SVi 






fa s 


*— h-i i_, ^ -— ^ w eg 


s O H 


s 




o 


o w ^ o> ^O 


ci cS 






aa 










ug 










& 5 

o S 


'-3 r 2 fr-S ■ "«• OT 








'k ^ o " x -- ^ "w 









a< 



^ — cS 

o ^P o 
C5 c £" 



O 
v. 

- 
fa 

fa 

o 

t» 

< 
o 
o 

03 

r ^ 
Eh 



1 


— 


_ 






ao 


- 




on 


03 


^ 


3 
3 




j: 




CD 


O 


— 


^ 


y: 


- 



•§..1 ° 

— M ~ ~ 



oR s o 
1 Bg 



!H & 



':r, ; 



'S " P i2 
cs^i -sS 

^3 <• Ot« 
- *J o 

<:^ ■*» a 
o to- 5 
O P ■- ° 

K a) ca _ 
o^ « C 
e- ^-s 3 c 



o 


« f- 


— ; 








PhcS 


p 


a> 


±1 w 


A 4 


^ 


a 




^^ 


!=J P 


-^ 





T« 


to 




42 a 


efl 


1 

fa 


§1 

c« Vh 

COrri 


> 
pi 


*s s 


^— ( 


►J 


^ 




^ i 


>i^3 




o 


co +2 




Ota 


PI 








iJl-S K 


DO 


fa 

KM 

W 


as 


-fa> 
cd 
CO 


p£l=wOO 


fa 








u o 

Art 


5 

o 



a p 

rt o 

0) 

O « 

O 

mO 



s s ° 

o§5g 



ag^ 



a 

w 
fa 
o 
p 



3faW > 
£fa 1 

-go cS ^ 
o JS 2 
w O °° 

c m £ 9 



i3.2,a 

►^ — ' CS 

I Id 

^-kOh^ 

W'^ ^-. © 
Eh » o 3 

-dfa I *-.<« 

CSQ Q O O 

03fagfa| 

^ U °S CO 

cS u _ ( v^ cr? M 
CD P5 Oc3 

„fa Eh ca P 

?0 "< ,9 o 

hSS OOco 



^ o^ 



O? 



c = o 

C C 3 

O C o 













H 




















O 




60 « 




















P w 






3 


--!•= 2 £ 


o 


~ ■ 3 "3 


o 

o 
_S 






Cfl 


fa 


" ? ' a ol -3 




— C 3 s S 




■: n e : -' = 




^ " w — - -^ 




3 — _ - _' 5 - 














r--^30B 




fac>icc -^iricoN 



'C rt H 



o « 



CD -*J 

13 



1 1 



be o> 



&o J 



s 



Ph 
CD 

a 

ta 
o 





n i; ^ ^ 
- 



M * 


n 




>> ^ 


3 










<» — . 




^w 



? n S 



> •« •= = Q 



p 

CD 

•i § 






!: t£ 

^ s 



9 d w -rt 4 



0> fl HH ^ 



■S -2 I 1 



o. 2 = 



= 


CO 


=N 


g 


S-, 


r& 


s 


— 
P 


r 



=G r ° ,2 fc. o 



S' — up the 1 
ut 4 miles sc 
Jenkins' Co 


-t- 


3 



o 


CS 

9 

o 

S3 

-= 


o 

= 
o 


DD 
CD 


- 
= 


: 
fa 


o 

IS 

1* 


a 

CD 


3 

o 


!* 2 •- 
fa's & 


a 


o 


— 
o 


0) 


3 


fa- 15 w 


a 
3 


ad 
O 


C 


da 

r. 


a 


o 




> 


o 




^ ^^ 


" 


r« 


g 


= 






i— i 


H 


o 


< 


^ 



cS 

s 


13 


- 


- 


i-r 


- 


CS 





ca 


E 
n 












5» 

Cii 

-/ 
CD 


CD 
P. 

C 


> 


CH 



t 

a 
ft 


p. 

i 


ca 


jS 


- 


a 


(j 


Cw 




- 


o 


cj 


- 


11 




3 
Q 


r . 




;• 


»4 

CD 


b 


- 


■0 . 


— 


« 


| 


*> 


p 


CD 


CD 


cj 


d 






H 










3 


5 


CO 














=» 




- 




;t 


j- 


~" 




•■ 


- 1 
5 






0. 






( 175 ) 



XV.— On Variability in Human Structure, with Illustrations, from the Flexor 
Muscles of the Fingers and Toes. By Wm. Turner, M.B. (Lond.), F.R.S.E., 
Senior Demonstrator of Anatomy in the University of Edinburgh. 

(Read 19th December 18C4.) 

Deviations from the usually described arrangements of the parts, of which 
the human body is composed, have from time to time attracted the attention of 
the anthropotomist. In many anatomical text-books, as well as in sundry 
memoirs specially devoted to the subject, numerous examples of such variations 
have now been recorded. To the scientific anatomist these have always had a 
certain value, but of late years this department of anatomical inquiry, more 
especially in connection with variations in the muscular system, has had 
additional importance and interest attached to it, on account of the attention 
which has been directed to the correspondence, or want of correspondence, in the 
muscular arrangements in man and the other mammalia, more particularly the 
apes. 

Into this aspect of the question it is not my intention to enter in this com- 
munication. My object on this occasion is rather to compare certain structures 
in one human body with corresponding structures in others, and to point out the 
extent of variability which may occur in similar parts in different individuals. 

Every one is conscious that of the multitude of individuals he may meet with 
in the course of a day's experience, no two are alike. Leaving altogether out of 
consideration all mental differences, each possesses some peculiarity of form and 
gait which enables him at once to be distinguished from those around him, and 
that these external manifestations of variability are in their prominent features 
correlated with internal structural differences will, I suppose, be generally 
admitted. That diversities in the shape of the skull, for example, occasion cor- 
responding diversities in the form of the head and face, so as to impart to them 
characters diagnostic not only of the race, but of the individual, have been 
recognised from the time of Blumenbach and Camper. But the osseous is not 
the only organic system in which distinct evidence of structural variability may 
be traced ; the muscular, vascular, nervous, and visceral systems all exhibit it. 
In some cases, undoubtedly, the departure from what may be termed the standard 
method of arrangement, as set forth by descriptive writers, is greater than in 
others, but evidence of its existence to a greater or less degree in every indi- 
vidual may be obtained not only by the examination of the systems taken as a 
whole, but of the separate structures of which they are composed. But though 
some of the best marked examples of internal structural variations are cor- 

VOL. XXIV. PART I. 3B 



176 MR WM. TURNER ON VARIABILITY IN HUMAN STRUCTURE. 

related with corresponding variations in the external configuration of the body, 
yet there are a large number which, either from their minuteness, or from being 
situated in the deeper seated parts, give no sign externally, and to distinguish 
them requires close and careful dissection. For many years I have been in the 
habit of preserving a record of the most remarkable " irregularities," as they are 
often called, which have come under my notice ; and I could cite many cases 
from my note-book in which, in the course of dissection, variations in the different 
organic systems were noted. During the present winter session, for example, 
four arms have been met with in which that very curious process of bone, 
known as the supra-condyloid process, projected from the inner part of the shaft 
of the humerus. In all, this process was connected to the inner condyle by 
a ligament. The process, the ligament, and the shaft of the humerus, covered by 
the brachialis anticus muscle, formed collectively the boundaries of a supra-con- 
dyloid foramen. In all the median nerve went through the foramen. So far 
these limbs, though varying greatly from the usual arrangement of parts in the 
human upper arm, corresponded closely with each other, but in other respects 
they differed considerably amongst themselves. In three specimens the pronator 
radii teres muscle arose from the process and the ligament connecting it to the 
condyle ; in the fourth the pronator muscle did not arise from these structures, 
but the ligament gave origin to some of the fibres of the brachialis anticus muscle. 
In one specimen the brachial artery, after giving off an accessory radial artery 
high up in the limb, accompanied the median nerve through the supra-condyloid 
foramen ; in another the brachial artery, after giving off its ulnar branch of 
bifurcation high up in the limb, also passed along with the median nerve behind 
the process; in the third, the brachial artery pursued its usual course along the 
inner margin of the biceps to the bend of the elbow previous to its bifurcation, 
and sent simply a small branch through the foramen along with the median 
nerve ; in the fourth not only was the brachial artery not deflected from its cus- 
tomary course, but it did not even send a small branch through the foramen, 
through which, consequently, the median nerve proceeded unaccompanied by any 
vessel.* In three of the specimens, also, a muscular slip arose along with the 

* The four cases described in the text of the occurrence of a supra-condyloid foramen in the 
human upper arm are not the only specimens which have come under my notice in the dissecting- 
room. In former years I had observed five specimens, in three of which both brachial artery 
and median nerve passed through the foramen, in the remaining two I had unfortunately not pre- 
served a note of the arrangement. But by far the most complete account of the anatomy of the 
supra-condyloid foramen which has yet appeared has been drawn up by Professor Wenzel Grueer 
in an elaborate memoir presented to the Imperial Academy of St Petersburg. Vol. viii. 1859. 
This anatomist has collected from the works of previous writers, as well as from material which 
has come under his own observation, sixty-two cases in which this foramen was noticed in the human 
body, and in which there was at the same time a greater or less amount of variation in the arrange- 
ment of the pronator teres, the median nerve, the brachial artery or some of its branches. One of 
the chief features of interest connected with the supra-condyloid foramen is the circumstance that 
it furnishes, as an occasional occurrence in human structure, an approximation to an arrangement 



MR WM. TURNER ON VARIABILITY IN HUMAN STRUCTURE. 177 

flexor sublimis digitorum from the coronoid process of the ulna. This slip ter- 
minated on a tendon, which in one specimen became blended with the tendon of 
the flexor profundus passing to the middle finger ; in another with the tendon of 
the same muscle going to the ring finger ; and in the third with the tendon going 
to the little finger. In the fourth specimen the flexor sublimis was not connected 
to the flexor profundus by any intercommunicating structures. In one specimen 
the middle, ring, and little finger tendons of the flexor profundus were connected 
together by a network of intertendinous bands ; in another such bands only con- 
nected the middle and ring finger tendons of that muscle ; in the remainder these 
structures were absent. In one of the specimens the abductor pollicis received a 
distinct slip of origin from the styloid process of the radius, whilst in another the 
abductor minimi digiti received a slender muscular slip, which arose in the lower 
part of the forearm from an accessory palmaris longus tendon. 

It would be quite possible for me to multiply examples to serve as additional 
illustrations of variations occurring in several of the most important organic sys- 
tems in the same body, — variations so well marked, indeed, that though, as in 
the cases above cited, it is probable no outward evidence of their existence was 
manifested, yet they furnished the individuals in whom they occurred with cha- 
racters as distinctive as any peculiarities of external configuration. Hence we 
may conclude that in the development of each individual a morphological 

which is very frequently met with in some of the Mammalia. For there has now been recorded a 
considerable number of instances in which a distinct canal, generally with bony walls, existed in this 
locality in various Quadrumana, in Galeopithecus, in the Edentata and Monotremata, in many Car- 
nivora, Marsupialia, Rodentia, and in some of the Pinnepedia ; whilst it would appear to be absent in 
the Ruminantia, Solidungula, Multungula, and Cetacea. But though the canal would seem to occur 
almost constantly in all the genera of some orders and families of the Mammalia, yet it by no 
means follows that in other orders and families, though it may occur in one genus, that it exists in 
all, or even though it may occur in one species of a genus, that all the species of the same genus 
should possess it. Thus, as Professor Owen has shown (Article Marsupialia in " Cyclopaedia of 
Anatomy and Physiology"), whilst it exists generally amongst the Marsupialia, yet it is absent in 
Dasyurus and Thylacinus ; and though most of the species of Phalangista possess it, yet it does not 
exist in Phalangista Coolcii ; and whilst Gruber saw it in Erinaceus auritus, he did not find it, and I 
have not seen it, in Erinaceus europceus. In the Pinnepedia also it has been described by various 
anatomists as present in the Phoca vitulina, and Gruber has seen it in other species of the same 
genus. In a common seal which I dissected, I found that it only transmitted the median nerve, 
neither the brachial artery, nor any of its branches passed through it ; in the Walrus (Trichechus), 
however, anatomists agree in stating that it does not occur, a fact which I have observed in three 
skeletons of that animal which have come under my observation. Again, in some of the Mammalia 
variations in its occurrence take place in individuals of the same species, a circumstance which has 
been noticed not unfrequently amongst the Quadrumana, though it has not as yet been seen, I believe, 
in the humeri of any of the Anthropoid Apes. Thus, whilst Tiedemann describes it as present in 
Cercopithecus sabceus and Cercocebus fuliginosus, Meckel and Otto state that it is wanting in those 
species; a discrepancy of statement which may probably be explained by regarding the arrangement 
as a variety present in one individual but absent in another. Of the skeletons of the Quadrumana 
personally examined, I have found the foramen absent in two specimens of the Orang, in a Chim- 
panzee, in two specimens of the Gibbon, in Cercocebus fuliginosus (agreeing thus with Meckel 
and Otto), in Macacus cynomolgus, in Cynocephalus maimon, Hapale jacchus, and Ateles paniscus ; 
whilst I have found it present in a species of Cebus, and in the prosimian Stenops tardigradus. 



178 MR WM. TURNER ON VARIABILITY IN HUMAN STRUCTURE. 

specialisation occurs both in internal structure and external form, by which dis- 
tinctive characters are conferred, so that each man's structural individuality is an 
* expression of the sum of the individual variations of all the constituent parts of 
his frame. 

But it is not essential that, for the demonstration of this specialisation of 
structure in the individual, "\ve should extend our inquiries over all the organic 
systems. Any one, if carefully examined, will afford us sufficient evidence of its 
existence. The muscular system is the one I have especially selected for illustra- 
tion. There are some parts of this system in which, from the mode of arrangement 
of single muscles, and from the manner in which they are collected into groups, 
we are enabled to study more precisely than in other localities the extent of varia- 
tion which is permitted, and the various forms which it assumes. None are 
better fitted for this purpose than the flexor muscles of the fingers and toes ; for 
not only can we define with great exactness the arrangement of these muscles and 
their tendons, but we can employ in connection with them a method of descrip- 
tion precise enough to convey a conception, not only of the stronger and best 
marked varieties, but of the more minute deviations from their usually recognised 
disposition. During the past twelve months, I have made a series of special 
dissections of these groups of muscles, and I shall now record the general results 
which I have arrived at in the examination of these parts. It must be under- 
stood that all the dissections were made on the bodies of the inhabitants of these 
islands, natives of either Great Britain or Ireland. 

The flexor muscles in the forearm and hand, to which my attention has 
especially been directed are the flexor longus pollicis, the flexor sublimis 
digitorum, the flexor profundus digitorum, and the lumbricales. The long flexor 
muscles exhibited numerous variations in their bulk, in the extent of their 
attachment to the bones of the forearm (the extent of the radial origin of 
the superficial flexor was especially variable), and to the interosseous or 
other fibrous membranes from which they arose. The superficial and deep 
flexors of the fingers also varied as to the mode in which they divided into their 
terminal bundles ; in some cases the division took place lower down in the fore- 
arm than in others. This was especially the case with the deep flexor, in which it 
was not unfrequent to see the separation between the more internal of its 
terminal tendons still incomplete at the carpal end of the forearm, or beneath 
the annular ligament. In one specimen in my possession, the muscle divided into 
five bundles, two of which afterwards united to form the tendon for the ring 
finger.* But, in addition, other variations were met with of a more remarkable 

* Multiplication of the bundles of tin's muscle has been recognised by Arnold, Henxe (Mus- 
kellehre, p. 196, 1858), and Theile (Traite de Myologie), 1843, p. 246. Theile also states that 
it sometimes receives a special head of origin from the inner condyle of the humerus ; and Theile, 
Hallett (Ed. Med. and Surg. Journ. vol. lxxii. p. 12), and Henle state that it sometimes receives 
fibres from the radius. 



MR WM. TURNER ON VARIABILITY IN HUMAN STRUCTURE. 179 

character. A more clear conception of their nature may perhaps be formed if we 
conceive the long flexors of the digits as composed of muscles situated on two 
planes, a superficial and a deep, and then bear in mind that both sets of muscles 
are subdivided into bundles, each of which terminates in a tendon possessing a 
distinct attachment to its proper digit. Now, between the different subdivi- 
sions of the muscle or muscles, situated on the same plane, and between the 
muscles situated on different planes, tendinous or musculo-tendinous bands not 
unfrequently proceed so as to connect them together. Thus, whilst it is custo- 
mary to consider the flexor sublimis as dividing into four distinct bundles, each 
ending in a tendon, I not unfrequently saw a tendinous or musculo-tendinous 
slip proceed between adjacent bundles, and keep up a lateral communication 
between the divisions of the muscular mass situated on the same superficial plane. 
In a similar manner, the divisions of the muscular mass situated on the deeper 
plane were not unfrequently connected together by lateral bands. In the flexor 
profundus digitorum these lateral connecting bands presented various arrange- 
ments in different individuals. Sometimes the three inner tendons were closely 
tied together in the forearm, either by simple bands passing from one to the 
other, or by a more complicated reticular structure. At others only the two inner 
tendons; at others again the tendons for the middle and ring fingers were intimately 
connected (fig. 1), whilst the little and index tendons were quite free. As a rule, 
indeed, the index tendon appeared to be less liable to form a connection with the 
tendon of the same muscle than was the case with the other sub- 
divisions of the flexor profundus. But on the other hand, I saw 
several specimens in which the index division of the deep flexor 
was intimately connected to the flexor longus pollicis,* a junction 
of considerable interest, as it approximates in their arrangement 
these muscles in the forearm and hand with the flexor hallucis 
and flexor communis digitorum in the foot. The nature of this 
union varied considerably in different specimens. In some it con- 
sisted of a muscular bundle, passing obliquely downwards from 
the fleshy part of the flexor of the thumb to the fleshy part of the 
index division of the deep flexor ; in others it consisted of a musculo- 
tendinous slip proceeding obliquely downwards from the muscular 
part of the former to the tendon of the latter (fig. 1) ; and in some of these 

* Various anatomists have recognised the occasional connection of these tendons, without, how- 
ever, specialising its different forms. See Theile, p. 246; M'Whinnie, Lond. Med. Gaz., vol. 
xxxvii. p. 191 ; Henle, p. 196 ; Wood, Proc. Roy. Soc. of London, p. 301, 1864. I am disposed 
to regard the connection in one or other of its forms as more common than is usually supposed. 

t Fig. 1, t, flexor longus pollicis; p, flexor profundus digitorum. It shows the connection of 
the index tendon of the latter muscle with a strong musculo-tendinous band from the former, also 
the close union for some distance of the middle and ring-finger tendons of the deep flexor. This, and 
the other illustrative figures, have been drawn from the dried preparations of my dissections by my 
pupil, Mr Richard Caton. 

VOL. XXIV. PART I. 3 c 




180 



MR WM. TURNER ON VARIABILITY IN HUMAN STRUCTURE. 




Fig. 2 * 



cases the connecting slip was in great measure, though not altogether, formed 
of the fibres of the rounded head of the flexor longus pollicis, which arose from 
the coronoid process of the ulna. In one case the connecting slip received almost 

one-half the fibres of the long flexor muscle, a specimen 
which illustrates how large and important this inter- 
muscular tendon may at times become. In one very 
remarkable specimen the bond of union passed in the 
opposite direction from those above described — viz., 
from the index tendon of the flexor profundus to the 
tendon of the flexor longus pollicis (fig. 2). 

Amongst the intermuscular structures which not 
unfrequently connect together the superficial and deep 
flexor muscles of the forearm, I am disposed to place 
that rounded musculo-tendinous band, which is so 
often met with, as a second head of origin of the 
flexor longus pollicis, for it arises along with the 
flexor sublimis from the coronoid process of the ulna, 
and ends inferiorly in the inner part of the long flexor of the thumb. But the 
superficial is also not unfrequently connected to the deep flexor of the fingers 
by intermuscular bands. For I have frequently seen a slip of muscle arise from 
the coronoid process, along with, and apparently forming a part of, the flexor 
sublimis, which, after it became tendinous, blended in five specimens with the 
tendon of the flexor profundus going to the little finger {e.g. fig. 2), in one with 
the tendon passing to the ring-finger, in four with the tendon of the same 
muscle going to the middle finger, and in one it divided into three slips which 
joined the deep tendons for the middle, ring, and little fingers. The blending 
usually occurred opposite, or slightly below, the carpal articulations. f 

The lumbricales muscles exhibit many forms of variation in size, number, 
extent, surface of origin, and mode of insertion ; but as both Theile and Henle 
have entered fully into these varieties, I need do no more than state that I have 
seen, in addition to most of the forms which they have described, a variety in 
which an accessory first lumbricalis arose tendinous from the flexor sublimis. 

* Fig. 2, t, flexor longus pollicis ; p, flexor profundus digitorura ; s, flexor sublimis digitorum. 
The connection of the first and second muscles by a tendinous band passing from the index tendon 
of the latter to the long flexor of the thumb, is shown ; also a tendon connecting the ulnar side of 
the superficial with the tendon of the deep flexor for the little finger ; also a close connection low 
down the limb between the ring and little finger tendons of both the superficial and deep flexor muscles. 

f The presence of slips proceeding between the flexor sublimis and F. profundus, though with- 
out precise statement as to their connections, has been recognised by Cowper (Myotomia reformata), 
Theile. and Wood. 

I may in this place also refer to an arrangement which I saw on one occasion in the left fore- 
arm. A slender fasciculus of muscular fibres proceeded from the flexor sublimis immediately to the 
inner side of the palmaris longus. It ended on a tendon which passed beneath the palmaris, and 
joined the tendon of the supinator radii longus at the lower end of the forearm. 



MR WM. TURNER ON VARIABILITY IN HUMAN STRUCTURE. 181 

After a course of about two inches it became muscular, and then ran parallel to 
the first lumbricalis, and was inserted along with it. 

The flexor muscles of the toes, the arrangements of which I have more especi- 
ally studied, were the flexor brevis digitorum, the flexor communis digitorum, the 
flexor longus hallucis, the flexor accessorius, and the lumbricales, — an important 
group of muscles, the different members of which are more or less intimately 
related to each other in the sole of the foot. In order to form as precise a con- 
ception as possible of their mode of arrangement in the foot I carefully dissected 
fifty specimens, taking them without selection from the subjects which came in 
my way in the ordinary course of my anatomical work, so that the variations 
described must not be regarded as unusual or abnormal forms. The results I 
have arrived at differ in many respects from the descriptions of these muscles 
usually given in treatises on anatomy. Of these fifty specimens no two were 
exactly alike, so that it would be necessary, in order properly to bring out the 
extent of individual variation which they presented, that each should have a 
separate description ; but as this would be tedious both to writer and reader, it 
may suffice if I adopt some method of arrangement which may exhibit their most 
important variations. 

In all the specimens the tendon of the flexor longus hallucis gave off, in the 
sole of the foot, a slip or band which connected that tendon either to one or more 
of the subdivisions of the flexor communis digitorum, or in part to that tendon, 
and in part to the flexor accessorius. In its size this connecting slip varied 
somewhat, and though at times flattened and membrane-like, yet was mostly in 
the form of a rounded band. In every specimen it took a more or less important 
part in the formation of the deep flexor tendons for one or more of the four outer 
toes. In eleven specimens it ended solely in the deep flexor tendon for the second 
toe ; in twenty specimens it bifurcated and ended in the deep flexor tendons for 
the second and third toes ; in eighteen specimens it trifurcated, and ended in 
the deep flexor tendons for the second, third, and fourth toes ; in one specimen it 
divided into four parts, and ended in the deep flexor tendons for the four outer toes. 

Of the eleven specimens in which the connecting band went solely to the 
second toe, it formed about one-half the deep flexor tendon for that toe in four 
cases (fig. 9), the remaining half being formed partly by the flexor communis and 
partly by the flexor accessorius. A much larger proportion than one-half in six 
cases (fig. 11) ; and in one case it and the flexor accessorius together formed the 
whole of the deep flexor tendon for the second toe, in the construction of which 
the flexor communis did not consequently enter (fig. 3). 

Of the twenty specimens in which the connecting slip went to the second and 
third toes, it contributed a larger share to the second than the third toes in 
twelve specimens, in one of which it formed, with the addition of a few fibres 



182 



MR WM. TURNER ON VARIABILITY IN HUMAN STRUCTURE. 



from the flexor accessorius, the whole of the deep flexor tendon for the second 
toe ;* it was divided almost equally between the two in six specimens (fig. 4) ; 
and in two specimens it and the flexor accessorius together formed almost the 
whole of the deep tendons for these toes, the share taken in their construction by 
the common flexor being limited to a few fibres (fig. 5). 

Of the eighteen specimens in which the connecting slip went to the second. 
third, and fourth toes, it contributed a larger share to the second than to either 






Fisr. 5. 



the third or fourth in seven specimens (fig. 6), in one of which the process for the 
deep flexor tendon of the second toe was much larger than that supplied by the 
flexor communis ; a larger share to the second and third than to the fourth in five 
specimens ; a larger share to the second and fourth than to the third in one speci- 
men ; and about equally to these three toes in the remainder. 

In the solitary specimen in which the connecting slip went to the four outer 
toes, the subdivisions for the second and third toes were larger than those for the 
fourth and fifth, that for the fifth being a comparatively slender thread (fig. 7). 

In none of the fifty specimens did the connecting band join the tendon of the 
common flexor previous to the subdivision of the latter tendon. In every instance 
it proceeded either single, bifurcated, trifurcated, or in four subdivisions, to its ap- 
propriate toe or toes, and in its course joined the divisions of the flexor communis, 
or the portions of the flexor accessorius passing to the same toe or toes. To 
the deep tendons for the second and third toes, more especially, it not unfrequently 
contributed quite as much as the flexor communis, and occasionally it and the 
flexor accessorius together, entirely or almost entirely, were substituted for 



* The flexor communis in this case trifurcated for the third, fourth, and fifth toes. 

t Fig. 3. In this and the succeeding figures, a, is the flexor hallucis longus tendon ; b, the 
flexor communis digitorum tendon ; c, the flexor accessorius. In figure 3 the flexor communis forms 
no portion of the deep tendon for the second toe, and after giving a slip to the flexor hallucis tendon, 
trifurcates for the three outer toes. 



MR WM. TURNER ON VARIABILITY IN HUMAN STRUCTURE. 



183 



the flexor communis in the construction of the deep flexor tendons for those 
toes. * 

In nine specimens a band, sometimes of considerable size, proceeded from the 





Fig. 6. 



Kg. 7. 



common flexor tendon previous to its subdivision, which joined the tendon of the 
flexor hallucis longus beyond the origin of the connecting slip for the common 

* That the tendon of the long flexor of the great toe gives off" a band more or less strong to the com- 
mon flexor of the toes in the sole of the foot has been almost universally recognised by anatomists, but 
the exact nature of the connection between them has not at all times been clearly expressed. Amongst 
the older anatomists, Vesalius describes this band as passing from the tendon of the great toe to the 
tendon proceeding to the second toe, and sometimes in an equal degree to the tendon of the common 
flexor for the middle toe. Diemerbroeck again states that sometimes the long flexor of the great 
toe is divided in the sole into two parts, one of which goes to the great, the other to the second toe, 
and then the common flexor sends but three tendons to the other toes. Cowper and Bidloo simply 
describe a connecting band passing from the proper to the common flexor, without specialising its mode 
of termination, and this method of description has been followed by most systematic writers in the latter 
part of the last century, and in the present, as Innes, Monro, Sabatier, Bichat, Boyer, John Bell, 
Fyfe, Cloquet, Cruveilhier, Dodd, Quain, Harrison, Hyrtl, Ledwich, Ellis, Knox, Holden, 
Heath, and Gray. Meckel employs, in his description of the long flexor of the great toe almost the 
same method as Diemerbroeck, but, in addition, states that the long flexor tendon for the second toe 
is for the most part formed by the connecting band and the flexor accessorius. Theile follows very 
closely the latter statement of Meckel, but, under the head of anomalies, he describes the connecting 
band as dividing for the second and third toes. Arnold gives the connecting band as strengthening 
the tendon for the second toe, though it often goes also to the third toe. Henle states that the strong 
process from the proper to the common tendon is for the most part, and at times altogether, continued 
into the tendon destined for the second toe. Mr Church, in a recent monograph on the myology of the 
Orang {Natural History Review, 1862), has also directed attention to the connection of the band from 
the flexor hallucis with the second and third toes. Professor Rolleston has advanced evidence to 
the same effect. Last of all, Mr Huxley (Reader, 13th February 1864) states, as the results of his 
dissections, that the tendon of the flexor hallucis longus, besides giving off the tendon to the great 
toe, furnishes distinct slips to the two or three succeeding digits, uniting with the tendons of the 
flexor digitorum and flexor accessorius. That considerable variability occurs in the mode of termina- 
tion of the connecting band might almost be inferred from the different descriptions given of it by the 
numerous anatomists just quoted, each apparently, of those at least who go into details, basing his 
description on the specimen or specimens he may more particularly have examined. A more exact 
conception, however, of the extent of this variability may be gathered from the analysis of the fifty 
specimens recorded in the text. 

VOL. XXIV. PART I. 3D 




184 MR WM. TURNER ON VARIABILITY IN HUMAN STRUCTURE. 

flexor tendon from it (figs. 3, 5, 8, 10). In these cases, therefore, the tendons 
were doubly connected by intertendinous bands* 

The flexor accessorius varied greatly in its mode of termination on the flexor 
tendons. In but a few instances (fig. 5, for example) could it be said to end in 
the manner usually described in the text-books, by joining the outer border and 
upper, and sometimes the under surface of the tendon of the flexor communis. 
In many cases it had no connection whatever with the outer border of that tendon ; 
in several of these it contributed no fibres to the tendon for the little toe, and in 
a few it had no connection with the tendons for the fourth and fifth toes. In 
other cases, however, it gave off a distinct tendinous or musculo- 
tendinous bundle, sometimes of considerable size, to the deep 
tendon for the little toe (figs. 3, 6, 7). In a few cases the deep 
flexor tendon for that toe was almost entirely (fig. 10), and in 
one case (fig. 8) apparently, entirely formed of a tendon pro- 
ceeding from the flexor accessorius, the common flexor tendon 
sparingly in the former (fig. 10), and not at all in the latter 
case (fig. 8), entering into its construction. In most cases the 
accessory flexor ended partly on the flexor communis, and 
partly on the connecting slip from the flexor hallucis, and 
through one or both of these contributed materially to the 
formation of the deep tendons for the second, third, and fourth toes. In one case 
it sent, in addition, a few fibres to the primary tendon of the flexor hallucis, and 
in another all its fibres terminated on the connecting slip, and through it were 
transmitted to the deep flexor tendons of the second and third toes. In one case 
it gave oft' a distinct slip, which, separating into two parts, gave one to each process 
of bifurcation of the tendon of the flexor brevis digitorum for the third toe. 

In two cases the flexor accessorius had an accessory muscle connected to it, 
which arose from the deep fascia of the back of the leg in its lower third, conceal- 
ing at its origin the posterior tibial vessels and nerve. It passed downwards, and 
ended in a rounded tendon, which extended through the inner ankle beneath the 
abductor pollicis, and joined the inner margin of the flexor accessorius (fig. 9)4 

* It would almost appear as if some of the systematic writers of the last century had recognised 
the band proceeding from the flexor communis to the flexor hallucis, but not the one passing in the 
opposite direction. Vide Albinus, Winslow, Tarin, Sandifort, and Douglas. Several of the 
more recent writers have described an arrangement similar to the one recorded in the text. — Vide 
Sabatier, Arnold, and Theile. 

f Fig. 8 shows the deep flexor tendon for the little toe entirely formed of the flexor accessorius. 
The flexor communis, after sending off a connecting band to the flexor hallucis, trifurcates for the 
second, third, and fourth toes, to which the connecting band from the flexor hallucis also proceeds. 

I The two specimens described in the text were found amongst the fifty specimens specially 
analysed, but I have in former years, and in other subjects, met with additional instances of an 
accessory muscle in this locality. The region of the inner ankle appears, indeed, to be frequently the 
seat of such accessory muscular structures, e.g. 



MR WM. TURNER ON VARIABILITY IN HUMAN STRUCTURE. 



185 




Fig. 9.* 



The lumbricales muscles presented many variations, some of the leading forms 
of which it may be advisable to particularise, more especially that Froment 
(with whom Henle seems to agree) states that variations in the arrangement of 
these muscles are extremely rare. The first lumbricalis, in the specimens under 
analysis, arose sometimes from the tibial side of the deep 
tendon for the second toe, after the junction of the connect- 
ing slip from the flexor hallucis with the division of the com- 
mon flexor tendon for that toe. Sometimes only from the 
tibial side of the connecting slip ; sometimes only from the 
division of the common flexor to the second toe ; in one case 
from the expanded part of the common flexor before it divided 
into its terminal tendons ; in other cases by a continuous origin 
both from the tibial side of the second toe tendon, and from 
the expanded part of the common tendon ; and in two cases 
by two distinct heads, — one from the tibial side of the con- 
necting slip from the flexor hallucis, the other from the 
expanded part of the common flexor before its division into 
the terminal tendons. In one case no lumbricalis was present in the first meta- 
tarsal space, but two were situated in the second space (fig. 8). In another case 
the second lumbricalis was absent. In several cases, not only did the second, 
third, and fourth muscles arise from adjacent sides of the tendons between which 
they were situated, but also from special slips derived from those tendons. 
Sometimes their fibres of origin extended for some distance backwards over the 
general expansion of the common flexor tendon. In other instances the fibres of 
the fourth lumbricalis, or of the third and fourth lumbricales, were continuous 
with (or received fasciculi from) those of the flexor accessorius ; in others they 

1st, A large slip springing from the inner side of the soleus, and passing quite distinct from the 
tendo Achillis, to be inserted into the inner concave surface of the os calcis. 

2d, A muscle arising from the deep fascia of the back of the leg, and inserted into the inner side 
of the os calcis, close to the inner head of the flexor accessorius ; this apparently constitutes the 
accessorius ad calcaneum of Gantzer. 

3d, Two muscular bundles connected to the deep fascia of the back of the leg, one as high as the 
middle of the tibia, the other close to the origin of the flexor hallucis longus from the fibula ; these 
bundles united to form a muscle which passed beneath the internal annular ligament to the sole 
where its tendon bifurcated, one slip joining the tendon of the flexor hallucis longus, the other the 
tendon of the flexor communis digitorum. A corresponding arrangement was found in both limbs. 

4th, A well-marked muscle arose from the deep surface of the soleus tendon. It concealed the 
tendons of the deep muscles, and the posterior tibial vessels and nerves in the lower third of the leg, 
and was inserted into the deeper surface of the tendo Achillis, immediately above the os calcis. A 
similar case to this has been described by R. Quain. 

Other irregularities in this locality have been recorded by Mayer, Rosenmuller, Gantzer, 
Meckel, Hallett, Theile, Henle, and John Wood. 

* Fig. 9. d, the accessory muscle to the flexor accessorius. It has been bent out of its proper 
direction so as to occupy less space in the wood block, e, the displaced fasciculus of the flexor 
brevis for the little toe, which simply blends, without bifurcating with the deep flexor tendon for that 
toe. 



186 



MR WM. TURNER ON VARIABILITY IN HUMAN STRUCTURE. 



received a special fasciculus of fibres, arising from the process sent by the con- 
necting slip of the flexor hallucis to the third or fourth toes ; in one case the 
fourth lumbricalis was absent. 

Variations in the mode of arrangement of the flexor brevis digitorum were 
also noted. The tendon passing to the little toe was sometimes not perforated 
by the tendon of the common flexor. In one case it was blended and inserted 
along with it ; in others it was so thin as to be lost in the fascia of the foot ; in 
one it was altogether absent. In five cases the short flexor tendon for the little 
toe was displaced at its origin, and arose from the common flexor tendon previous 
to the subdivision of that structure (fig. 10).* At its origin it either consisted 
partly of fibres continuous with those of the common flexor tendon, and partly 
of distinct muscular fibres attached to and springing from that tendon, or it 
arose tendinous, and then muscular fibres appeared in it, which again terminated 





on the tendon of insertion. In three of these cases the tendon bifurcated, to 
allow the common flexor tendon for the little toe to pass through and beyond 
(fig. 10); in the other two it blended with the common flexor tendon for that 
toe, and was inserted along with it (fig. 9). In one specimen the tendon for the 

* Fig. 10. In this drawing, /is the flexor brevis digitorum, which divides into fasciculi for the 
second, third, and fourth toes, the fasciculus for the fifth toe, e arises from the tendon of the flexor 
communis. In this figure the deep flexor tendon for the little toe is formed almost entirely from the 
flexor accessorius, the flexor communis contributing but a few fibres. The connecting slip from the 
flexor hallucis trifurcates for the second, third, and fourth toes, and the flexor communis gives off a 
connecting band to the flexor hallucis. Brugnone, Meckel, Theile, Htrtl, Henle, Church, and 
Huxley, have all recognised the occasional origin of the short flexor tendon for the little toe from 
the flexor communis. In another subject I saw the fasciculus forming the short flexor tendon for 
the little toe arise in part from the external inter-muscular septum, and in part through fibres con- 
tinuous with the muscular part of the flexor accessorius. 

t Fig. 11, g, the tendon of the flexor brevis for the third toe, its junction with a slip from the 
expanded part of the flexor communis is represented. In both feet of a subject not included in the 
above analysis, I saw an arrangement similar to that represented in fig. 11, except that the slip 
from the common flexor tendon bifurcated before joining the two branches of bifurcation of the flexor 
brevis. 






MR WM. TURNER ON VARIABILITY IN HUMAN STRUCTURE. 187 

third toe received a strong tendinous slip from the expanded part of the common 
flexor tendon, and the two were blended and inserted together (fig. 11). In 
another, the short flexor tendon for the third toe received an additional slip 
from the flexor accessorius. 

In the foot, therefore, as in the forearm and hand, intermuscular structures 
not unfrequently connected together not only the flexor muscles situated on the 
same plane, but those situated on the superficial and deeper planes. 

The fifty specimens of the flexor muscles of the foot, the special analysis of 
the mode of arrangement of which I have now recorded, will be sufficient, I think, 
to show that in the construction of this group of muscles an amount of variation 
existed much greater than might at first sight have been supposed. In a portion 
of one muscle alone, viz., the connecting band from the tendon of the flexor 
hallucis longus, a considerable number of modifications occurred. In the flexor 
accessorius also great variability was displayed, and in some proportional relation, 
apparently, to the extent of variation in it and the connecting band, did the 
flexor communis digitorum undergo certain modifications in its arrangement, so 
much so, indeed, in certain cases, as to permit those structures to be to a great 
extent substituted for it in the formation of the deep flexor tendons for some of 
the toes. 

Variability in the construction of parts, however, was not manifested merely in 
different individuals, but in the same individual the corresponding structures on 
opposite sides of the body were by no means symmetrically disposed. Thus, in 
two of the four examples recorded in the earlier part of the paper in which a 
supra-condyloid process existed, it occurred only in one arm of each subject in 
two cases; whils in a third subject, though both humeri exhibited the process, 
yet the relations of the brachial artery to it on the two sides were by no means 
symmetrical. The tendons in the left foot, in many of the individuals in whom 
both feet were examined, varied also more or less from those in the right foot, so 
that in the construction of the limbs, as well as in the form and arrangement of 
the organs contained in the great cavities of the body, an asymmetrical disposi- 
tion of parts is to be looked for. Thus, we arrive at the conclusion that the plan 
on which the human body is constructed, although constant in all its essential 
characters, yet admits of variations (within itself as it were) in certain directions 
and within certr.in limits. Neither form nor structure is absolutely stereotyped, 
but modifications occur which, when regarded singly, may be considered, perhaps, 
as slight and of comparatively little importance, yet when viewed collectively, 
are sufficient to give to the individual well-marked distinctive characters. 

Much has been said and written of late years on the existence of structural 
differences between the fair and coloured races of mankind, more especially be- 
tween the white man and the negro,— differences which, according to some 

VOL. XXIV. PART I. 3 E 



188 MR WM. TURNER ON VARIABILITY IN HUMAN STRUCTURE. 

writers, are so great as to constitute an actual specific distinction between them. 
But those who have advanced and supported this view seem to me to have 
ignored, or at least not to have taken sufficiently into consideration the fact, that 
in the white races themselves, nay, as we have shown in this paper, in a limited 
section of them even, variations occur in the arrangement of certain of the soft 
parts so great as to permit of the office usually performed by one muscle to be, in 
a great measure, or even altogether, exercised by another. But the extent of 
variation which the white races may exhibit is by no means exhausted by what we 
have detailed in this communication. Numerous isolated examples of variations, 
both in the muscular and other systems, have been recorded elsewhere by my- 
self and other anatomists, and additional observations in the same profitable field 
of inquiry will, I have no doubt, add many other forms to our already extensive 
list. Until, however, the deviations from the usually described arrangements in 
the fair races are more systematically inquired into than has hitherto been the 
case, we cannot hope to reach an accurate conception of the latitude which may 
be allowed them. 

Of the extent of the structural variability which may exist in the soft parts 
of the dark races, we as yet know but little. It is seldom that their bodies have 
been critically examined ; and of many of the coloured races, indeed, the number 
of dissections has been too small to permit of any satisfactory conclusions to be 
arrived at, for opportunities of making the necessary observations seldom fall in 
the way of the European anatomist. His dissections are made and his descrip- 
tions are based on the examination of the inhabitants of his own continent. Our 
knowledge of the comparative anatomy of the soft parts of the races of men is 
still in its infancy. To make good, indeed, the proposition that the negro is speci- 
fically distinct from the white man, it would be necessary to show that any 
peculiarities of arrangement which may be exhibited in the construction of his 
body, are either constant, or, if variable, that the variations are not in accordance 
with those which have been or may be met with in similar parts in the bodies of 
men of the fair races. For until we have determined not only the amount of 
structural variability in the different races, but the comparative frequency of 
occurrence of its principal forms, we shall not be in a position even to discuss 
the question of specific difference on anything like positive scientific data, still 
less to pronounce dogmatically on the subject. 

From the special difficulties which surround the study of human anatomy, 
it will not be an easy matter to determine with precision the laws which regulate 
the development of these structural variations. In some cases, indeed, it would 
appear that a variation in one structure is not unfrequently correlated with 
variations in adjacent parts. Thus in the four specimens described in the early 
part of this communication in which, in conjunction with a supra-condyloid pro- 
cess, a foramen existed above the inner condyle of the humerus, the median nerve 



MR WM. TURNER ON VARIABILITY IN HUMAN STRUCTURE. 189 

passed through that foramen. The deflection of the nerve from its course and 
the existence of the process were, it is evident, not only from these but from 
many similar cases, correlated events. Again, in the flexor tendons of the foot, 
a deficiency in the size of the flexor communis digitorum was not unfrequently 
correlated with an increase in the size of either the connecting-band from the 
flexor hallucis, or of the flexor accessorius, or it might be of both; and an 
absence of a tendon from the flexor brevis digitorum for the little toe was not 
unfrequently correlated with the presence of a fifth tendon from the flexor com- 
munis digitorum. 

To how great an extent the conditions of life of the individual, in whom these 
and other varieties present themselves, may be concerned in their production, or 
how far they maybe transmitted from parent to offspring, and thus be considered 
as family peculiarities, are questions which for the present at least must be left 
undetermined. But in regard to the variations in the muscular arrangements 
which have been specially illustrated in this communication, it may safely be 
stated that the power of performing the appropriate movements of the part must 
be modified in accordance with the modifications in its structure. 



PLATE W.Roy al Sac .traiu EdzrhYolIZLV. 



fiOROLOCICAL CHART OF EUROPE 

lor SAM. Or/vh-r JO'!' 1863 




l^piaitatioiL; _ 

Zzn&s of equal barometric presstirv 
Lutes oftqvwi thernwmctric disturbance 
Winds, liaht. t -»/iv'n.\ , ff.iifi orhurriaajte 

Ike arrows fly tvitn.-thev.ind. Calm. © 
Ootid. C: fop F: blue sky or few clouds & rain at 8 A.M. R 
tin sojTuturie in previous 24 hours T. 



FLATEMVRoyoL Soc. trans.Edm.yol.XXli: 




ETEOROLOGICAL CHART OF EUROPE 

For 8 AM. October 31^1865 



'^l-kkJchrislon Sdin' 



-- 

IP- A*-. 

'kV 



PLATE .IT Royal Soc. tra7is.EdjtrbYol.HIV. 




Tft&yA_£Jeftn*to7vJEtiuir 



rJkA 



£jl Hi! 



j 



FLATJEXl 7 Ro vol. Soo. trans Edm TolMJV. 



EOROLOCICAL CHART OF EUROPE 

For 8 A.M. FovemJ>er2 #" 1863 






.<o 



North Cape 



^' 



28.X 



z«f» n 



97\ 28;8 



Valad 




Explanation,:— 

Zituzs of equal iarometriiz pressure 



Zbles "t'equuj thsrmt'nictrrj- disturbanae _____.. 

' Winds, liaht ^.strong^-*.fiales or~hun-iixjiLe^^ 

The arrows flywtijbtiiowaul. Calm © 
Clrtiut C,j;y FM/j. „7.t orftwahwdz linunatSAM.R 
Rain somjiim,. i/iprevious llliours T. 



<^3 



18 '■■- ;'.'.ljurt.'ri Jij>t r 



PLATE XVILRoyal Soc. tnms.Edun.Vol. .ffl V. 



iOROLOCICAL CHART OF EUROPE 



1h 



For 8A.M. November 10™ 1863 






,«0 



North Cape 



4J?J 



■^■/6 



oSaparaaday 



Christian. siauL 



Werrvosandyo 



■SharZaiuL 




Chris 



1 Petersburg 



2tfN 



Moscowo B 2^s 



r altmLiiL^ 



Putbus. 



.''Br 



/'!• 



x J?L\'mDictfiZ 


ML* 


7 


,12 

V 


sou 
R \ 


•/} 




>r * «" 


ti? 


,»-" 


x \ 






■4Tb 




\ R 


- 


|l» 




NoFarls'' 


C 


»''el 


-V-, 


K^P 


55 


• ,*'' , 


'' 








-EWo 



Ce 



3Tikolaie\' 



'Hilbai 



Madrid 

°B 




Explanation : _ 

f equal barvmgti-ir firessur< 



Tintsaf equal thermometris distiu-bajtce — 

Wiruls. light ^strcruj^-r.guUs orfourrioaju^+ 

llu arrows fb$ \\ith-th?*ijrd. Calni © 
Cl.nui C, . F. blue sky or few clouds B. rain at 8 AM R 
Baaisamauiie uLjirevwtts 24 hours T. 



e*ds* 8 



'W^lSJohjut^n. Zdu>-' 



TIATEMLRoyoL- Soc. trajxs.Ectm.Vol.IIJV. 



OROLOCICAL CHART OF EUROPE 

For 8A.M. November!!^ 1863 




Ike arrows fly with the wind. Calm 
Clou. i C fop f: bbwsky orfewdouds B, rain.at8A.lLK 
Rain somOzinp injwcvious 2 4- hours X. 



^.^JiJcl-atJta^Xaa-r 



'*-' •'& 









METEOROLOGICAL CHART OF EUROPE 



FLATE 'HZ Royal Soc.trcuis.EolbvVolA 





rovemhrr3 r d 1H63 




Fm- 8 AM. jV manher 4 € ,!- 1863 




METEOROLOGICAL CHART OF EUROPE 




FIATJEU. Royal Soc. trans EdxnJol J 



I 





.^^asea Level, at 130 places in Europe, from 28th October 10 12ib Sovember, from 20th to afiih November, from 30th Nove, 
FABLE r-ShoTrii* the B A i<o> ICT iuc Prb^l-ee, -n Engl^h meUe., reduced to W jj™^ ^ ^ ^ [q jm ^^ at 8 A . M . 



30. 31. I. 2. 3. 



tlrligulua (EnslnnJI, i 



CWhoiHg 

Simabams, . . . 
| 

M»SJ!Ii4 f '. i i 
sujrii • • ■ ■ 






^f TABLE II.— Showing the Temperature (Fahr.) and State of the Sky in the Morning at 110 Places in Europe, from 26th October to 12th November, from 20th to 2Cth November, from 30th November to 

5th December, and 14th to 18th December 1863. 
^K—B represent* blue aky, or eky little more than half covered with clouds ; C, a much clouded or overcast aky ; F, fog ; R, rain at the time of observation ; and r, rain sometime during the previous 24 hours. 



■\i 



26. 87. 28. U. 30. i 



8. 9. 10. 11. 



a. 3. 4. 6. 14. 15. 



s: : 






TABLE III -Showing for 69 places in Europe the Deviations from the Mean Temperature (Fahr.) of each day from 26th October to 12th November, from 20th to 20th 

November, from 30th November to 5th December, and from 1-ith to 18th December 1863. 

Note.— The Temperatures marked with a minus sign are under the Mean, the others are above the Mean. 



iBSJM.m 


OCTOBER. 


NOVEMBER. 












DECEMBER. 




28. [ 27. | 28. 


29. 


30. 


31. 


1. 


2. 


3. 


4. 


5. 


6. 


7. 


8. 


9. 


10. 


11. 


12. 


20. 


21. 


23. 


23. 


24. 


25. 


28. 


30. 


1. 


2. 


3. 


4. 


s. 


14. 


15. 


16. 


17. 


18. 










„ 


B 





„ 


- 2 
8 


7 
7 


. 


- g 


o 


4 


— 7 


. 




- i 


11 




8 


G 


- i 


19 


13 


6 


6 


- 1 


; 


3 


6 


7 


7 


- 1 


l 


"1 


QrcencaaLlc, . . . 
Valencia, .... 


1 

G 


2 


- 4 


1 


- 1 


- 2 


- 2 


- 1 


6 


7 


7 


2 


- 4 


2 


- 2 


- 3 


9 




6 


5 




6 


10 


G 


4 


1 


1 




5 


5 


11 


■ 


" 


■ 1 


Beam, an v. 
Breswiy, 


3 


1 


- 1 


- c 


- 4 

■ J 

- 6 

- 4 


- 2 

- O 

- 3 

- O 


- 2 

- 2 

- r. 

- 4 


- l 


- 2 
_ 1 



2 


- 3 

- 2 


- G 

- 2 





- 6 

- 2 


- 7 

- 7 


1 

2 


- 


1 


8 
9 


8 
9 


7 
8 


8 
6 


7 
G 


G 

7 


9 

6 


4 


4 


- 3 


- 4 

- 4 


7 


4 


■5 


5 

6 


3 
1 


" • 


e 


Stornaway, .... 

KW» 


- 2 

- 1 


- 
1 


- 5 
G 


- 3 


-11 
- 4 


- 7 

- e 


3 

7 


- 6 

- 3 


-In 
- 8 


- 1 

- 6 


- 8 

- 2 


- 8 

- 4 


- 3 

- 2 


- 5 

- 6 


— 6 

— 3 


8 
4 


12 


4 
6 


6 
3 


G 


In 
B 


LO 
11 


1 


3 


- 3 
3 


- 1 


4 


8 
13 


G 
G 


6 


11 


1 


a 


Bkoi,an... 

Holy ("«'], . . ■ ■ 
Pomljroko, .... 
Ywnimitfi, , . . . 


I 


2 

3 
3 
- 


3 


- 3 



- 4 

_ 1 


1 
4 


- 3 


- 3 

7 


2 

- i 


9 


3 
3 


- 8 

- 4 


- G 

- 3 


- 1 
2 


- 3 

7 


1 
3 


- 3 


- 4 


1 


14 
9 


7 

in 


e 

:i 


11 
11 


I! 


17 
18 


- 6 


1 
11 


1 
9 


- 1 
6 


6 

11 


12 

11 


II 
19 


8 
13 


4 
8 


§ 


1 


3 

2 

— 3 


3 
2 
G 


1 
7 
4 



3 



- 3 

- 3 


-3 


1 
2 
6 


2 

7 

- 3 


ii 

III 

2 


4 
9 

G 


1 


- 1 


6 

7 

- 8 


i 


4 
2 


4 

5 

- 6 


2 

- 1 

- 6 


3 

- 1 

- 6 


11 
9 
4 


7 


2 


M 

9 

8 


10 

8 

7 


13 

1:1 
hi 


14 
14 
9 


G 
4 

3 


8 
9 


6 
9 

:■ 


3 
3 

1 


6 
G 


11 

in 
11 


19 

12 
3 


11 

11 

4 


9 

7 


8 
3 


1 

- 3 

2 


- 




3 


1 


3 


- 2 


- 2 


- 2 


- 4 


13 


9 


- 6 


1 


6 


- 2 


- 8 


- 9 


- 7 


G 


111 


3 


1 


10 


13 


10 


11 


3 


;i 


r, 


- G 


ft 


- 1 


3 


ft 


1 


- 4 


Wcj it!'. 

Panww 


o 


fi 


3 


3 


1 


- 2 


- 2 


1 


9 


8 





7 


9 


- 2 


3 


1 


- 4 


7 


11 


8 


10 


12 


12 


11 


4 


9 


in 


7 


:; 


n 


9 


9 


11 


ft 


- « 








2 


3 


2 


- 3 


- 2 


- 2 


4 


7 


7 


6 


7 


5 


1 


1 


- 1 


- 3' 


10 


9 


7 


8 


G 


11 


10 


7 


10 


3 


11 


4 


9 


9 


9 


8 


D 


- 1 


Norway annHivenkh. 

ii >ii .1 ni'i ■, . . . 
Hornimiiri'l,. . 
Chrinliiiiisitml, 
Bkadumux, .... 

Ohriatiunin, . . . 

Stock (ml in, .... 




] 


2 


13 


12 


13 


14 


8 


3 


8 


1 


- 1 


3 


2 


- 9 


- 9 


8 


14 


6 


G 


-19 


- 7 


-21 


-2.1 


17 


16 


17 


18 


18 


21 


•7: 


ii 


_ 


- 8 


11 


a 


o 


- fi 





8 


13 


13 




G 


4 


8 


6 





1 


- 3 


- 4 


- 1 


6 


8 


13 


19 


2 


- 4 


- 6 





10 


11 


16 


7 


1G 


17 


18 


I 


11 


ii 


ir, 


n 


3 


3 


4 





9 


9 


4 


1 


6 


G 


2 


- 1 


4 


- 3 


- 2 


7 


2 


4 


18 


16 


11 


9 


10 


11 


12 


11 


- 3 


111 


16 


■1 


14 


7 


11 


ft 


a 


1 


10 





G 


G 


G 


4 


G 


4 


7 





4 


- 1 


G 


- 4 


- 7 


6 


3 


3 


12 


19 


10 


7 


8 


12 


13 


3 


6 


7 


6 


6 


12 


4 


8 


12 




1 


o 




6 


10 


5 


G 


G 


- 2 


7 


G 


3 


- 4 


1 


- 6 


- 6 


7 


- 2 





13 


19 


12 


3 


2 


9 


13 


3 


G 


7 





G 


11 


2 


:i 


19 


D 




- 1 


C 


3 


6 


8 


3 


- 1 


- 4 


4 


4 


4 


1 


- 4 


1 


-13 


- 3 


1 


1 


8 


7 


11 


6 


4 


4 


11 


G 


7 


G 


II 


8 


11 


- 8 


11 


7 


10 


- 4 


-11 


- 4 


1 


2 


6 


7 


4 


l 


2 


1 


- 1 


- 7 


- 7 


- 9 


-15 


- 8 


- 6 


- 5 


13 


12 


6 


G 


~ 2 


G 


4 


9 


G 


7 


11 


1 1 


1 1 


- 6 


2 


ft 


14 


1 


ROBSlA. 

Arolian^i'1, .... 
fit Pete railing, ■ ■ 

Mowuiv 


- D 


4 


8 


5 


4 


) 


G 


5 


G 


- 2 


8 


G 


Q 


- 2 


- 1 


-10 


-21 


8 


4 





-17 


-19 


-20 


-17 


10 


13 


16 


1G 


7 


-14 


3 


3 





-11 


-12 


- 6 


- 1 


1 


:i 


- 4 


- 8 


3 


2 


8 


6 


4 


9 


2 


- 3 


- 1 


- 3 


- 7 


- 1 





14 


1G 


11 


18 


12 


10 





11 


10 


10 


3 


3 


4 


- 2 


K 


- 2 


- 3 


11 


ii 


■ a 


- 4 


1 


- 2 


l 


4 


6 


1 


8 


! 


2 


- 


- 2 




- 9 


- 1 


4 


14 


13 


12 


12 


4 


1 


- 1 


It 


" 


2 


- 4 


- 4 




- 4 


2 


- 9 


2 




■ IS 


- 3 


- 7 


- 


- 7 


4 


- 7 


■ 3 


2 


- 1 


11 


2 


1 


- 


- 6 


-17 


1 


G 


10 


1 


17 


13 


18 


17 


21 


11 


8 


14 


8 


-in 


-10 


111 


1 


- 


-11 




Wnmtw, .... 


- 3 


-13 


-11 


- 8 


- 3 


in 


G 


7 


9 





19 


6 


- 2 


1 


-10 


- 7 


- 2 


4 


12 


1 


1 


8 


10 


10 


11 


2 





- a 


- G 


1 


1 


- 3 


1 


- 3 


8 


in 




H 


1H 


II 


1 


-22 


-18 


- 


- 4 


II 


I" 


4 


3 


- 6 


- 3 


- 8 




- 7 


4 


11 


10 





- 1 


- 2 


7 








:i 




- 1 


- 2 




II 


1:1 


10 






- 4 


-11 


-10 


hi 


-20 


1- 


- 6 


3 


7 


11 


- 3 


G 


2 


3 


- 6 


- 7 


- 8 


1 


G 


9 


2 


10 


12 


3 


- 4 


-"» 


- 11 


- 9 


11 


3 


- S 


- 1 


4 


-11 


-17 


- 17 


DlNMAIlK. 










































































Copenhagen, . . . 


- 2 


1 


2 





G 





2 





3 




3 


- 3 


- 


-10 


- 8 


- G 


- 4 


2 


7 


7 


8 


10 


8 


10 




3 


1 


- 3 




6 


- 


- 3 


- 


■1 


1 


- 1 


- 6 


5 


- 3 


1 


4 


1 


1 





1 


9 


G 





1 


1 


- 3 


- 4 


- 1 





4 


3 


9 


11 


In 


8 


6 


1. 


- 6 


:'. 


4 


4 


7 


10 


13 


II 


7 


-1 


PaoiwiA. 










































































K ( .ni f ,"ilit>rn, . . , 


■i 


- 7 


- 8 


- 4 


4 


c 


5 


2 


4 


6 


8 


- 1 


1 


- 4 


1 


- 


- 6 


- 4 


5 


2 


3 


9 


8 


9 


7 


i; 


- 


- 2 


- ii 


1 






- 


1 


4 


■1 


PutllllH 


:i 


- 2 


- 2 


3 





3 






1 


7 


■1 


- 1 


1 


- 1 


- 4 


- G 


- 3 


- 


3 





4 


9 


9 


6 


4 


- 2 


- 4 


- 6 




4 


2 


(i 


10 


10 




1 


Pftdcrliom 


- 4 


- 2 


- 


8 


in 


3 


3 


2 


2 


11 


T 


- 2 


- 2 


- 2 


- 4 


- 7 


- 2 


- 7 


8 


3 


10 


6 


10 


14 


12 


- 8 


- G 


1 


4 


G 


7 


hi 


9 


8 


a 


1 


SrOrltlLII, 


- 2 


- 7 


- 2 


•J 


fi 


G 


5 


4 


8 


C 


12 


- 1 


■1 


2 


- 7 


W 


2 


1 


G 


G 


8 


8 


10 


10 


8 


- 3 


- (i 


- G 


I 


6 





3 


11 


10 





11 


Aiothian Empiiik. 


































































* 








Prague 


B 


- 8 


r. 


- 


5 


7 




2 


3 


8 


111 


3 


11 


- 1 


- 1 


- 6 








2 


3 


3 


6 


7 


9 


7 


- 4 


- G 


- 8 


G 


G 


2 


8 


13 


9 


7 


S 


Onwow, 


■ 3 


- Ii 


-I" 


- 7 


1 


7 


■1 


- 


6 


4 


in 


1 


- 4 


- 3 


- 7 


- 8 


2 


3 


4 





1 


2 


7 


8 


8 




- 6 


- 9 


- 5 


2 


- 1 


- 2 


2 


2 


2 


(1 


Vienn 


I 


- r. 


- 7 


- 6 


1 


5 


3 


:■■ 


G 


- 5 


111 


11 


i: 


- 


G 


- 7 


- 1 


2 


3 


1! 


2 





1 


3 


4 


- 9 


- 6 


- 


- 4 


- 1 


6 


8 


11 


8 


2 


D 


Kroiiimiiniistur, . , 


- 7 


- 5 


II 


— 2 





G 


4 


:■■ 


2 


ii 


13 


7 


- 


- 


_ 2 


- 


2 


3 


3 


- ii 


- 3 


- 2 


4 


5 


10 


- 7 


- 7 


- 6 


1 


4 


3 


10 


12 


6 


s 


s 


Kliigonfiirt, . . . . 


-10 


-10 


-11 


- 6 


- 1 


7 


in 


- 3 


- e 


11 


- 4 


- 4 


G 


- 6 


- 7 


- 9 


- 8 


- 2 


3 


- G 


- G 


- 5 


- 1 





2 


- 3 


- 3 


- 6 


1 


4 


3 


13 


14 


10 


10 


14 


Griiuan States, 










































































I">ii«iK 


-10 


- 7 


Hi 


2 


14 


4 





— 2 


— 2 


7 


6 


- 5 


— 7 


- .1 


- 8 


-10 


- 4 


- 4 


2 


- 2 


G 


3 


7 


5 


G 


- 8 


- 8 


- 6 


3 


3 


3 


7 


9 


8 


fi 


- 1 


Munifli, 


- 7 


- 7 


- 2 


8 





7 


1 


2 


1 


6 


11 


4 


1 


7 


3 


- 2 


- 


- 3 


- 2 


- 2 


6 


12 


12 


12 


11 


- 6 


- 6 


- 


7 


1 


1 


111 


111 


5 


I 


D 


SwiTr.Kui.Asn. 










































































Annul, 


- 4 


- 2 


2 


7 


11 


4 


- 1 


- 3 


- 1 


4 


8 


4 


4 


8 


4 


- 


- 2 


- 3 


- 4 


- 3 





9 


11 


7 


6 


- 3 


- 2 


- 3 


G 


- 1 


- 3 


7 


1 





1 


:i 


Geneva, 


- 2 


- 1 


1 


C 


11 


9 


- 3 


- 2 


3 





1 


- 2 


1 


4 


2 


- 1 


- 4 


- 4 


- 4 


- 7 


3 


11 


7 


4 


4 


- 3 


- 4 


4 


8 




- 3 








11 


1 


3 


Nktmkiu.and*. 










































































GtoniiiKi'ii 


-11 


-10 


- 6 





2 


2 


1 


- 3 


2 


10 


4 


1 


2 


- 1 


- G 


11 


- 2 


- 7 


- 2 


— 1 


7 


7 


7 


12 


6 


- 9 


-14 


- 


1 


7 


4 


12 


10 


11 


8 


3 


Holder, 


-11 


- 4 


- 6 





3 


2 


2 


- 3 


3 


8 


5 





1 


- 2 


- 3 


-15 


- 1 


- 4 


- 1 


- 7 


6 


7 


6 


9 


8 


- 9 


-12 


- 3 


1 


2 


7 


9 


8 


10 


7 


6 


Brloii'm. 










































































Brussels 


-12 


-14 


- 


1 




5 


- 2 


- 


- 1 


10 


10 


4 


- 8 


3 


- G 


-13 


- 6 


- 9 


- 


1 


G 


4 


6 


13 


11 


- 13 


-10 


5 


G 


4 


1 


G 


3 


4 


2 


- 1 


[•"RANCH 
lliivrv, 

Ohoibourg, .... 

Brest, 

L'Orieitt, . . . . 

Paris, 

Btruauouig, . . . 

RoehiWt, .... 

RaVOtllli'. . . 

Montftubftn, . . . 
Marsi'illi's 


- 1 


- 1 


1 


5 


2 


2 


- 2 


2 


2 


8 


5 


G 


5 


8 


2 


- 3 


2 


- 1 





4 


6 


4 


8 


8 


5 


- 7 


- 1 


— 9 


8 


3 


6 


In 


ft 


G 


11 






4 


1 




6 


2 


- 2 


- 2 





9 


7 


2 


7 


C 


4 


- 4 


- 3 


3 





4 


3 


1 


8 


6 


G 


1 


2 


6 


4 


3 


7 




7 


ft 


6 


I 


- 4 

- 3 

!' 

-10 

- 6 

- 6 
5 


- 7 

-10 

:. 

7 

- 8 
2 

- 6 
6 


- 1 

7 
1 
1 
1 
6 
O 
7 


3 
3 


1 
3 


- 3 


- 7 

■ B 


- II 

- 8 




:i 


5 
4 


4 
2 


3 


3 


3 


- 3 

- 5 


- 4 
-13 


- 1 

- 4 


- 5 

- 8 


- 

- 4 


7 


- 1 

- 5 


1 
- 2 


7 
6 


7 
4 


2 



- G 



6 
6 


3 

4 


4 

Ii 


- 1 

- 8 


6 
4 


G 
3 


11 

- 11 


5 
- 3 


1 
- G 


- 2 

- 3 


4 
- 1 

4 

II 
7 


- 1 
9 

8 


- 3 

6 

l 
8 

8 


- 3 
8 

- 3 

2 
6 


- 2 
Ii 

- 3 


- 

- 8 


- 3 
4 

- 6 


- 3 

- 3 


8 
6 
1 

- 1 

1 


8 
11 

ii 

- i 

- 2 


G 
9 


- 2 

- 6 

- 4 



1 

- 

- -1 
G 


7. 
8 

"i 

2 

u 


- 5 
8 

- 4 

- 9 

- 2 

11 




- 9 

- 2 

- 6 

- 1 


- 9 
2 

- 4 

- 

- 7 

- G 


- 4 

- 1 

- 2 

- 6 

- 6 


- 9 

- 

- 4 

- 9 


- 7 
1 

- 2 
3 

- G 

- 2 


G 

2 
3 
3 


4 
16 
G 
3 
3 
5 


G 
13 
2 
3 
3 
6 


6 

14 

- 1 

1 

9 


11 
G 
11 

2 
G 


-10 

- 2 

- 1 

- 1 

- 2 


- 8 
3 

- 1 
G 
3 
1 


6 

2 
8 
8 
7 
5 


9 
12 

12 

1' 
2 


- 3 

9 

- 3 
5 

- 2 

- 1 


- 2 
7 

- 7 

- 2 

- '■ 

- 7 


2 

6 
3 


3 
10 
G 
6 

- 11 
1 


1 

11 
.'. 
3 
- 3 
6 


1 

7 
6 

1; 

- 11 

1 


- 1 
10 

G 
4 

- I 

- 3 


Spain and Portuhal. 










































































Lisbon, , . . , . 
Boroolona 


6 
4 


8 

4 


1 
G 


3 
8 



6 


fi 
3 


3 
2 
11 


1 
1 

2 

- 5 
6 


- 4 

- 3 

O 

- 6 




- 3 

- 4 


- 3 

- 9 
2 


4 

- 2 


- 4 

- S 


3 

1 


1 



8 
3 
2 
4 

2 
6 


- 1 
2 


- 5 

- 2 


-°2 


- 

- 


7 
- 


9 
3 


9 



4 



6 
7 


"7 


4 

2 


G 
1 





6 
G 


G 
6 




- 1 


- G 

- 4 


11 
- 9 


-11 

- 6 


- 5 

- 


•\ 


Alicante 

Ban Fernando, . . 
Pnlma (Miyowa), . . 


7 
3 
7 


s 

4 


3 


4 
2 

7 


3 
2 
6 


-1 


s 


- 4 




- 4 
1 


3 

- 4 

4 


— 1 

1 

- 3 


- 3 

- 7 

- 8 
3 


- 3 

- 2 


- 2 

- 3 

- 2 

- 2 


- 1 

- 9 
2 

- 1 


3 

- 1 

7 




2 
4 
12 
1 


4 

2 
G 
4 


11 
- 2 


G 

- 7 

G 

3 


8 
7 
7 
3 


4 
6 
8 



7 

2 

G 

- 1 


11 

:> 
G 


3 
6 
2 
1 


.1 

- 6 

- LO 


1 

- 7, 

- 11 


1 

- 6 

- 3 


1 
- 7 

1 


- 3 

- 7 

1 


- 4 

- 8 
2 

- 4 


Africa. 












































































3 


7 


8 


4 








2 


- 2 


- 1 


1 


2 


- 


- 2 


- 


- 3 


— 5 


-11 


1 











4 




2 


.. 


3 


10 


9 


6 


'1 


1 


1 


1 


- 3 


- 6 


Italy. 












































































3 
- 6 


:> 


- 3 

-12 


3 
- 4 


8 

- 1 


10 


l 


7. 


4 
3 


- 4 


- 4 


- 4 




- 5 

- 

- 1 


G 





- 4 


- 5 

- 5 


- 5 


- 9 


- 6 


- 2 


- 


- 2 




- 1 


- 4 


3 


- 6 




- 


2 


2 





5 


2 


Napta, '.'.'.'. '. 


- 6 




- 8 




- 3 


- 6 


1 


i; 


2 


— 5 


- G 


- 4 

- 1 








— 11 


-13 


-14 


- 4 


4 


- 5 


- 4 


- 3 


- e 


- 4 


- 2 


- 4 


-10 


- 4 


-14 


-11 


2 


Puli'ruui (Sicily), . . 





- 1 


- 1 


" 2 


3 


1 


4 


4 


1 


- 


- 


- 





2 






- 3 


— 8 


— 6 



- 2 


- 4 

- 2 


- 3 

- 5 


- 2 


- 2 

- 2 


- 6 


- 5 


- 6 

- 5 


- 3 

- 2 


2 

2 


- 5 


- 3 

- 


- 

- 1 


- 2 

- 1 


- 1 

- 1 


-■ 
- 


Turkey. 










































































DonatantinQplo, . . 




-14 


-14 


-11 


- 


- O 


- 4 





4 


4 


5 


1 


_ , 








9 














































































3 


4 


S 


4 


2 


2 


- 7; 


3 


.1 





3 


1 


- 


- 4 


- 2 


- 3 


7 


Greece. 










































































Athens, 


- 6 


-s 


-• 


- 9 


- 3 


2 


- 


8 


4 


4 


3 


9 


2 


1 


4 


6 


7 


4 





° 


- 1 


3 


4 


1 


1 


- S 


- 8 


-10 


- : 


- 4 


1 


- 6 


- 7 


- 


3 


6 



u . . t( u Painfall each Day in English inches, at 36 places in Europe, from 26th October to 12th November, from 

TABLE 'V.-S.-in^A^of^Kau^l.^ch £*J g ^ ^^ ^ ^ ^ ^ ^ ^^ ^ 



flrwiiciwtlc, 

(Jul way, 

VllllNIL'ijI, . 

Quoeiutown, 

RffiiAwn 

I'., | v.n. 
Bandwii k, 
Btoi '"'J. 



I'iv.l A III 

Silloth, 



L'Orii-'iit, 
I ■: . . ■ h - 1 ■ ■ : . 

Dijon, . 



Klr».sl,v. 
Kiwtniniii, . . 
Lou^im, ■ ■ 

Ort'iiluiiii};, . 
Slul.msl , 
Ciitlii'i'iui'tiliiHLrK. 



Kl;r : ,.,l 



iwiraanLAHD, 

Aitruti 

Gouqvd, . 

JPAtS ash PORTDOA] 
Uabon. . 
Madrid. , 



2 


3 


,'.<i 


■13 


•Ml 


III 


■44 


3ii 


Ir. 


•24 


■02 


H3 


III 


U-, 1 


in; 


■lis 


in 


■10 


■iti 






■33 


■II 


■ill 


•70 


III 


112 


-411 


■:,ii 


■12 


IIM 


■33 


■M 


II 


mi 


■:,i i 


■47 


■10 


■42 


■07 


■mi 




Ml 


-", 


MS 


■71 


■87 


■32 


■in 


■in 


I" 




■Ifl 


■11 


•30 


.39 


•to 


•20 


■4:1 


•30 


nil 


III 


•10 


■27 


•08 


■0B 




■05 


•02 


■29 


■02 






1)1 




■44 



26. 30. 1. 2. 



TABLE V.— Showing the Direction and Force of the Wind in the- Mornine: ot 126 places in Europe, from 20th October to 12th November, from 20th to 20th November, from 30th November to 5th December, nnd from 
14th to 18th December 1803. Light nir to* a moderate breeze printed thus, wot : n fresh breeze to a. fresh gale, WSW ; a strong gale or hurricane, NNE. 



Heligolui'l (England), 






i/oriont, - ; ; : 
&.; : ■ ■ 

Itochfert, . . 






ontpllicr, , 






p.i™ ot sicii,),. : 



( 191 ) 



XVI. — Examination of the Storms of Wind which occurred in Europe during 
October, November, and December 1863. By Alexander Buchan, M.A., Secre- 
tary to the Scottish Meteorological Society. (Plates XIII. to XXI.) 

(Read 3d April 1865.) 

A brief account of the weather of this period as regards temperature was 
read before the Royal Society last year. It was drawn up at the request of Pro- 
fessor Balfour, to accompany his paper " On the Remarkable State of Vegetation 
in the Edinburgh Botanic Garden in December 1863." 

From the 26th of October to the end of December the weather was in every 
way remarkable. Though frost occurred in the end of October and beginning of 
November it was not severe, and the temperature continued on the whole season- 
able till the 12th of November. From this date till the end of the month it 
ranged unprecedently high, being 9° above the average temperature of the season. 
It then fell for the next ten days, but on no occasion below the average ; and 
again rose considerably above the average during the week ending with the 18th 
of December. Under this genial weather vegetation in the open air advanced 
rapidly to a state of forwardness not usually seen till the month of March. In 
December 245 plants were in flower in the Gardens in the open air, and of these 
35 were spring flowers. The frost which had occurred was insufficient to 
damage, to any material extent, 210 autumn-flowering plants; and the high 
temperature of November, which was as high as what ordinarily occurs in the 
beginning of May, brought the spring flowers prematurely into bloom, so that 
there was to be seen the rare spectacle of sweet peas and hepaticas flowering 
together. 

Thus, then, the atmosphere during this time was in a most abnormal con- 
dition in respect of temperature, which, of all the elements concerned, plays the 
most conspicuous "part in destroying its equilibrium. It is not surprising, there- 
fore, that the weather was equally remarkable, or even more so, for storms. 
From the 27th October to the 18th December, eleven well-marked storms passed 
over Europe in succession. 

Since the space embraced by storms frequently includes the greater part of 
Europe, it is only recently, owing to the extension and growing popularity of 
meteorology, and the countenance now happily given to it by most European 
governments, that sufficient data could be obtained for a satisfactory treatment 
of the subject. For the observations of the principal observatories of Europe are 

VOL. XXIV. PART I. 3 F 



192 MR ALEX. BUCHAN ON THE STORMS OF WIND WHICH OCCURRED 

too few in number, and at too great distances apart, to enable any one to lay 
down the isobarometric lines and general course of the winds, without drawing 
largely on conjecture and imagination. The recent multiplication of meteorolo- 
gical observatories is a great step in advance toward the discovery of the law of 
storms. 

Observations have been received from 135 places scattered over Europe, from 
the Mediterranean to Archangel in the north of Russia, and from the extreme 
west to the Ural Mountains. All parts of Europe are pretty well represented 
except Central Russia, the south-east of Austria, and Turkey. The following are 
the sources from which the observations have been obtained : — The places in Scot- 
land have been selected from the stations of the Scottish Meteorological Society; 
and most of the places in England and Ireland from Admiral Fitzroy's Tables, 
published daily in "The Times,"— the omitted observations on Sundays having 
been, to some extent, supplied by the observers themselves. Most of the con- 
tinental stations have been taken from the lists given in Le Verrier's bulletins 
of the weather, published daily in Paris, and from the " Meteorologische Jaarboek" 
of Dr Buys Ballot of Utrecht. I am further indebted to Dr Ballot for his 
valued assistance in supplying me with additional observations to those printed 
in the Jaarboek. The observations from Russia were kindly furnished by M. 
Ferdinand Muller, assistant in the Physical Central Observatory of Russia ; those 
from Sweden, by M. Bonnier, Stockholm ; those from Norway, by M. C. Fiarnley, 
director of the Observatory, Christiania ; and those from Denmark and Greenland, 
by Professor Holten, Copenhagen. Rev. Francis Redford supplied the obser- 
vations from Silloth ; Mr E. J. Lowe, those from Nottingham ; Mr W. C. Burder, 
those from Clifton ; Mr Henry Denny, those from Leeds; Mr William Johnston, 
those from Banbury ; Captain Williamson, those from Dublin ; and Mr A. 
Dickey, Queen's College, those from Belfast. The importance of observations 
from Iceland and Faroe was not overlooked, but we regret to say that no obser- 
vations were made in those places during the period. I beg also to return my 
most grateful thanks to the Marquis of Tweeddale and Baron Brunow for the 
interest they took in this inquiry in procuring some of the most valuable of the 
observations, especially those from the north of Europe. 

Construction oj the Tables and Maps. 

The observations at the different places were made at 8 a.m. At the few 
places where they were made at a different hour, such as 9| a.m. at Dublin, a 
slight correction was adopted to bring them into accordance with the others. 
The amount of this correction was deduced from the preceding and succeeding 
observations at the place, modified by the apparent course and rate of motion 
of the storm, as suggested by the observations of neighbouring stations. It 
not being necessary for this inquiry to descend to the thousandth of an inch of 



IN EUROPE DURING OCTOBER, NOVEMBER, AND DECEMBER 1863. 193 

barometric pressure, or parts of a degree of temperature, the tables and maps 
may be accepted as representing the pressure and temperature of the air over 
Europe, with scarcely any deviation from the truth 

The barometric observations (Table I.) were brought to English inches, and then 
reduced to 32° and sea-level. Each observation, so reduced, was entered in its 
place on the map, and lines were then drawn through all those places where the 
pressure was equal. These isobarometric lines are given for every two-tenths in 
the difference of the pressure,— for 30-5, 303, 301, 299, &c, inches. 

The lines of temperature have been laid down on a different principle. For 
lines exhibiting the actual temperature would fail to show, in a sufficiently clear 
manner, the real bearing of this important element, since the isothermals of 
October, November, and December run in a very irregular manner over the con- 
tinent of Europe. Hence not the actual temperature, but the difference between 
the actual temperature and the mean temperature of each day at the several 
stations is traced on the maps. 

Dr Buys Ballot has calculated the mean temperature of many places in 
Europe for every alternate day of the year, and for a few other places ten-day 
means. The results were published in 1861, in " La Marche Annuelle du Ther- 
mometr e et du Barometre en Neerlande et en Divers Lieux de V Europe." In the 
observations of temperature in the " Jaarboek," 1863, not the actual temperature, 
but the deviations from the mean temperature of each day, are alone given. These 
I have adopted simpliciter. Of the other stations, I have calculated the mean tem- 
perature of each day, using for this purpose Dr Ballot's tables, Professor Dove's 
mean temperatures, as given in " Darstellung der Wdrmeersclieinungen durch 
Funjtdgige MitteV 1863; the same author's " Monats-und-Jahresisothermen" 
1864 ; and the data in the Scottish Meteorological Society's " Proceedings" bear- 
ing on the subject. The differences between these daily means and the daily 
observed temperatures are entered in Table III., in which the minus sign shows 
that the temperature was under the mean ; and if no sign is used it was above 
the mean. The stations are pretty well distributed over Europe, and are suffi- 
ciently numerous to show the changes of temperature which occurred near the 
earth's surface before, during, and after the successive storms. They were entered 
on the maps, and then, as in the case of the barometer, lines were drawn through 
those places where the differences were equal. They show where the tempera- 
ture was the average 0°, and then in succession where it was 4°, 8°, 12°, &c, 
above the average or below it. 

The temperatures as actually observed are given in Table II. 
The state of the sky with respect to rain, cloud, and fog is indicated in Table 
II. by means of letters — R showing that it was raining at the time of observa- 
tion ; C, that at least three-fourths of the sky was covered with clouds ; B, that 
the sky was either quite clear, or not so much as three-fourths covered ; and F, 



194 MR ALEX. BUCHAN ON THE STORMS OF WIND WHICH OCCURRED 

that fog prevailed. When r is attached to any of the above letters, rain fell at 
that station sometime during the previous twent} r -four hours, but was not falling 
at the time of observation. The state of the sky at several places was not known. 
These places are marked with an asterisk, and R in such cases means that it rained 
sometime during the previous twenty-four hours ; but whether it was raining at 
the time of observation or not cannot be learned from the returns. 

The direction of the wind (Table V.) is indicated on the maps by arrows re- 
presented flying with the wind. The force of the wind is shown (1.) by plain 
arrows — >, which represent light air to a moderate breeze ; (2.) by arrows 
feathered on one side only ^-*, which represent a fresh breeze to a fresh gale ; and 
(3.) by arrows feathered on both sides >-*, which represent a strong gale, storm, 
tempest, or hurricane. A calm is shown by O. In the tables the force of the 
wind is shown by the different types employed, as there explained. 

The observations comprehend four periods, viz., (1.) from the 2Gth October to 
the 12th November ; (2.) from the 20th to the 26th November ; (3.) from the 30th 
November to the 5th December; and (4.) from the 14th to the 18th December 
— in all thirty six days. Maps were constructed, as described above, for each of 
these days. A selection from these accompanies this paper Plates XIII. to XVIII. 
give the barometric pressure, the temperature, the state of the sky, and the 
winds, as observed on the mornings of the 30th and 31st October, and the 1st, 
2d, 10th, and 11th November. Plates XIX. to XXI. give only the observations 
of the barometer and winds on the mornings of the 28th and 29th October, the 
3d, 4th, and 12th November, and the 1st, 2d, 3d, 4th, 5th, 16th, and 17th 
December. 

Observations of the Barometer. 

The observations of the barometer are the most important of all the observa- 
tions, since it is within the area where the barometer falls to some extent below 
the average that storms occur. Speaking roughly, the mean atmospheric pres- 
sure for these months is 29 9 inches. Therefore, the space comprehended within 
the isobarometric line 297, and the other lines showing a less pressure, may be 
called, for convenience' sake, the area of low barometer. Hence, while we trace 
the progress of these low pressures over Europe from day to day, we trace at the 
same time the progress of the storms. 

A brief account of these lines is desirable, to give some idea of the extent 
and course of the storms. An area of low barometer occupied the greater portion 
of the northern half of Europe, from the 28th October to the 9th November, 
during which time its eastern limit advanced slowly and steadily eastwards from 
Norway to the Ural Mountains ; while its southern limit, having first oscillated 
backwards and forwards over the space lying between Spain and Ireland, ulti- 
mately moved northward, and left Europe by the North Cape. During this time 






IN EUROPE DURING OCTOBER, NOVEMBER, AND DECEMBER 1863. 195 

four storms passed across this disturbed area, which was generally about 1900 
miles in length by 1400 in breadth. 

Storm I. on the 28th October (Plate XIX.), embraced the British Islands and 
the west of Norway, having its centre at Elgin, where the pressure was 29-41. On 
the 29th (Plate XIX.), the area of low barometer now included the north-west 
of France, the north of Germany, and the whole of Denmark and Scandinavia. 
The centre of the storm was near Christiansund, in Norway, and on the follow- 
ing day had passed out of the map by the North Cape. 

Storm II. had advanced so far by the morning of the 29th October (Plate XIX.) 
that its centre had all but approached the west of Ireland, where the pressure was 
28-56, being nearly an inch lower than the depression which accompanied the 
previous storm. On the 30th (Plate XIII.), it had arrived at Shetland, the lowest 
pressure being 29-44. At that moment the whole atmospheric system of Europe, 
to use a familiar illustration, appeared to be swinging round Warsaw as a centre, 
in the direction of the motion of the hands of a watch, so that in the south and 
south-west barometers were everywhere rising, whilst in the north and north- 
east they were falling. On the 31st (Plate XIV.), it had advanced eastward to 
Christiania. At the same time the isobarometric 28 -9 had greatly extended its 
area, and a new depression (II. b) had been formed in its western part, due west 
of the former, and contiguous to it. On the 1st November (Plate XV.), the iso- 
barometric 28 - 9 had contracted to one-half of its former dimensions, the two 
depressions in the centre had united and advanced a considerable way to the 
north-east ; and on the 2d (Plate XVI.), it may be observed further to the north- 
east, and to be now leaving Europe by way of Lapland. 

Storm III. had its centre, on the 1st November (Plate XV.), apparently within 
a hundred miles of the west of Ireland, where the pressure was 28-9. On the 2d 
(Plate XVI.), it had travelled east to Liverpool. On the 3d (Plate XIX.), it had 
continued its eastern course, and was now on the west of Jutland. At the same 
time the area of the storm had contracted to a fourth part of its former diameter ; 
and the lowest pressure of the centre, instead of 28 - 9, was only 29-3. It was 
thus giving unmistakable signs of wasting away, and next morning (Plate XIX.), 
it had quite disappeared — a wide space between the barometric lines at the 
entrance of the Gulf of Finland being all that remained to show where it had 
died out. 

The general features of the other storms were similar to those already de- 
scribed. The storm of the 10th and 11th November, and the storm in the begin- 
ning of December, had, however, certain peculiar features of their own to which 
I shall briefly advert. 

The chart for the 11th November (Plate XVIII.) is the most remarkable of the 
charts, and the more so if compared with that of the 10th (Plate XVII.). Though 
the barometer fell a little to the N.E. at the head of the Gulf of Bothnia, yet the 

VOL. XXIV. PART I. 3 G 



196 MR ALEX. BUCHAN ON THE STORMS OF WIND WHICH OCCURRED 

great fall took place to the S.W. To so great an extent did this occur, that the 
whole atmospheric system of Western Europe must be considered as having re- 
treated on its course, and to have travelled from the N.E. to the S.W. As the 
translation proceeded, the depression widened and deepened, and a new depres- 
sion was formed. The depression near Shetland, circumscribed by 29-3 on the 
10th, and measuring 410 by 250 miles, increased to 1100 by 550 miles on the 
11th, and the pressure in the centre was two-tenths of an inch greater. The 
isobarometric 29 5 had changed its position in a most remarkable manner. Its 
distance from 29 3 was greatly increased in Great Britain, and a new storm (VI.) 
was formed in the interval, 300 miles in diameter, having its centre near Plymouth. 
A little to the north of this, a space of about the same extent was noted for its high 
temperature on the 10th. The isobarometric 29 • 7 had also changed to a position 
equally remarkable, leaving a large space between it and 29 5 from Sardinia 
northwards ; and in the interval a depression was formed round Genoa. On the 
12th the two northern depressions had coalesced, and the isobarometric 29*3 con- 
tracted to a fourth part of what it was on the 11th, and the whole driven back- 
ward toward the N.E. The southern depression had travelled to the N.W., tripled 
its area, and was one-tenth of an inch lower. 

The storm in the beginning of December will be afterwards described under 
the head of the " Direction of Storms." 



Form of Storm Areas. 

The forms of forty-two different areas circumscribed by the isobarometric 
lines admitted of examination. Of these, thirty were either circular or slightly 
elliptical. In ten cases, the major axis of the ellipse was nearly double the length 
of the minor axis, and in one case it was three times the length. In two in- 
stances, 29-5 on the 11th November, and 29 3 on the 3d December, the outline 
of the areas was very irregular, owing to the occurrence of two central depres- 
sions in one case, and three in another, within it. It follows from this, that the 
storms most commonly assumed a circular or oval form, and that the ellipses 
were seldom much elongated. 

The area over which the storms spread themselves was very variable in size, 
being seldom less than b'00 miles across, but often two or three times that 
amount. This area was not constant, even as regarded the same storm from 
day to day, but varied in size, sometimes contracting and sometimes expanding. 
If it contracted, the central depression at the same time gave signs of filling up, 
and the storm of dying out. On the other hand, if the area widened, the central 
depression generally became deeper, and occasionally was broken up into two or 
more separate depressions, which appeared to become separate storms with the 
wind circling round each, as shown in the maps for 11th November and 3d and 



IN EUROPE DURING OCTOBER, NOVEMBER, AND DECEMBER 1863. 197 

17th December. These different depressions, however, soon reunited, and the 
storm proceeded as before. 

Direction in ivliicJi the Major Axis of the Storm Area lay. 

The direction in which the major axis of the storm lay, could be determined 
on twenty-eight occasions. On seven occasions it pointed to the N.E. ; on six to 
the E. ; on five to the N.N.E. ; on four to the S.E. ; on three to the E.N.E. ; and 
on three to the N. In most cases the major axis was coincident, or nearly coinci- 
dent, with the direction in which the storm happened to be moving at the time. 
These two features of storms have important bearings on the prediction of storms, 
and on the direction and veering of the wind. 

It has been sometimes affirmed of the European storms that they are 
constantly marked by a barometric depression stretching in a north and south 
direction over Europe ; but the analyses of these storms given above show that 
this assertion, in these cases at least, receives no support from fact. 

Direction in which the Storms advanced over Europe. 

The direction in which the storms advanced from the position they occupied 
on one day to the position they occupied on the next day, could be ascertained 
in twenty-four cases. In eleven of these, the progressive movement was to the 
N.E. ; in four to the E. ; in four to the S.E. ; in two to the E.S.E. ; and one to 
the E.N.E., S.S.E., and S.W. Thus, twenty-two travelled towards some point 
in the quadrant from N.E. to S.E., and only one took a westerly direction. 
Hence, these storms travelled as often toward the N.E. as toward all other points 
of the compass put together, and almost every one toward some point between 
N.E. and S.E. 

The storms seldom proceeded in the same uniform direction from day to 
day. Though generally the change was not great, yet occasionally it was so. 
Thus of the many interesting features which marked the storm of the beginning 
of December, none were more remarkable than the sudden changes of its progres- 
sive movement. I have added in the Appendix observations relative to this 
storm at shorter intervals of time than 24 hours. From these it appears that the 
centre of the storm on the 2d was near Liverpool at 9 a.m. (Plate XX.) ; Worcester 
at noon ; Oxford at 3 p.m. ; Cherbourg at 6 p.m. ; and Oxford at 9 p.m. The greater 
number of observations at 9 p.m. show three depressions : — 1st, at Shetland, 
28-88 ; 2d, at Oxford, 28*89 ; and, M, in Holland, 29-22. It is very probable that 
the storm had separated into two parts near Liverpool, one of which took a north- 
easterly course toward Shetland, and the other a south-easterly course toward 
Cherbourg. At 9 a.m. of the following morning (Plate XX.), the first had advanced 
to the N.E. to Christiansund ; the second had advanced northward to Shields ; and 
the third had advanced eastward to Denmark. At 9 p.m. of the 3d, the first was 



198 



MR ALEX. BUCHAN ON THE STORMS OF WIND WHICH OCCURRED 



no longer visible, having probably left Europe by the North Cape, while the second 
had advanced to the north of Holland. At 9 a.m. of the 4th (Plate XXL), it had 
advanced to Copenhagen, had greatly diminished in area, and the central de- 
pression was five-tenths less than on the previous morning ; and at 9 p.m., the 
observations at Christiania, Kiel, and Konigsberg show that the atmospheric 
equilibrium was restored, and the storm consequently had died out. 

Most of the storms left Europe by the North Cape or the north-east of Russia ; 
but two of them (Storms III. and X.) wasted away and died out before reaching 
Russia. 

Rate at which the Storms travelled. 

The distance between the points indicating the centre of the barometric 
depression, or the centre of the storm on two consecutive days, could be deter- 
mined on twenty-one occasions, which are given in the following table : — 





For Twenty-four 


Distance travelled 




No. of Storm. 


Hours, ending 


by Storm iu Eng. 


Rato per Hour. 




8 A.M. 


miles in one day. 




Storm I. . . . 


Oct. 29 


580 


24 


„ II- 








30 


600 


24 


„ II. 








31 


420 


18 


„ II. 








Nov. 1 


400 


17 


„ II. 








2 


420 


18 


„ HI 








2 


400 


17 


„ HI. 








3 


430 


18 


„ HI. 








4 


510 


21 


„ iv. 








5 


700 


29 


„ iv. 








6 


470 


20 


„ iv. . 








7 


360 


15 


„ iv. 








8 


470 


20 


,. v. 








11 


260 


11 


„ v. 








12 


390 


16 


„ VII. . 








22 


460 


19 


„ VII. . 








23 


560 


23 


,\ ix. 








Dec. 2 


500 


21 


„ IX. . 








3 


390 


16 


„ ix. . 








4 


425 


18 


„ XI. 








17 


485 


20 


„ XL . 








18 


460 


19 


Means, . 




461 


19 



Hence, the mean distance the storms travelled each day was 460 miles, 
being at the rate of 19 miles an hour. The least distance was from the 10th to 
the 11th, being only 260 miles, or 11 miles an hour. It was on this occasion 
that Storm V. retrograded toward the S.W., and the distance given is in all like- 
lihood too small, it being probable that it did not begin its retrograde motion till 



IN EUROPE DURING OCTOBER, NOVEMBER, AND DECEMBER 1863. 



199 



sometime after 8 a.m. of the 10th. Hence, 15 miles per hour may be accepted as 
the minimum rate per hour travelled by any of these storms. The greatest 
distance travelled on any day was from the 4th to the 5th, being 700 miles, or 
29 miles per hour. 

If Storm VI. really overtook Storm V. by the morning of the 12th, its pro- 
gressive motion must have far exceeded any of those in the table, since it must 
have travelled, in twenty-four hours, at least 1050 miles, or 46 miles an hour. 
The following observations, in addition to those given in the table, bear on this 
interesting point : — 

Table showing the Barometric Pressure and Direction of the Wind at 
Twenty-Four Places, at 8-9 a.m., 2 p.m., and 8-9 p.m. of the 1 1th Nov. 1863. 















c 
_bp 




a 


fcb 




CD 








r^' 


a 




d 


cfl 


rbi 


'3 


'C 




c3 


,_; 


llth November 1863. 


,_; 


_o 


te 


CD 


13 


."£ 


O 


O 






o 


o 
o 






cS 

m 


o 

a 

h 
o 

02 


CD 

H 
O 

Ph 


o 

3 
Q 


Ph 

CD 


B 
CD 
CD 

o 


o 
02 


"a 
g 

p 


cS 


a 
1 


;- 

CD 

> 

3 


( Barometer, 


2909 


29-14 


29-29 


29-14 


29-23 


29-22 


29-36 


29-46 


29-34 


29-30 


29-39 


29-38 


8-9A.M. . , 


























I Wind, . . 


WNW 


w 


w 


w 


vv 


w 


NW 


E 


w 


Calm 




sbyw 


C Barometer, 
























29-44 


2 P.M. -!„,., 


























(Wind, . . 


... 


... 


... 


... 


... 




... 








... 


NW 


( Barometer, 


29-30 


29-40 


29-53 


29-47 


29-38 


29-36 


29-53 


29-55 


29-52 


29-46 


29-51 


29-59 


8 - 9pM tww, . . 


























NWW 


N 


w 


w 


NW 


w 


NW 


N 


N 


Calm 


w 


WNW 




s 














bi 






c3 


M 




c£ 

















a 






^ 




rd 




o 


be 




CD 




3 






'3 


CD 


llth November 1863. 


b£> 

a 


13 






CD 


be 


3 


a 


8 




_C3 


en 

bo 






o 


CD 








CD 




3 












CfH 


CD 


p3 




p 




M 




0^ 




B 




o 


M 


f-i 




CD 






pi 


e3 




M 


:o 




fz? 


O 


o 


s 


w 


5 


P 


l-H* 


Ph 


M 


o 


M 


r Barometer, 


29-45 


29 38 


29-39 


29-50 


29-41 


29-43 


29-47 


29-68 


29-53 


29-45 


29-35 


29-67 


8-9 A.M. _ . 


























1 Wind, . . 


... 


NNE 


E 


sw 


w 


s 


sw 


NW 


SE 


sw 


ssw 


SE 


r Barometer, 




29-39 


29-38 


29-42 


29-43 


29-43 


29-39 












2 P.M. I . , 


























I Wind, . . 




Nbyw 


NE 


s 


sw 


s 


sw 












„ „ f Barometer, 


29-61 


29-60 


29-56 


29-48 


29-46 


29-47 


29-46 


29-43 






29-24 


29-59 


8-9 p.m. { TTr . , ' 


























I Wind, . . 


NNW 


WNW 


w 


s 


SE 


s 


s 


sw 


SE 


sw 


SE 


S 



At 12 noon, the pressure at Paris was 2939, and wind S.S.E. ; and at Luxem- 
burg 29-52, and wind S.W. From these observations, it is probable that this 
storm continued to advance southwards for an hour or two after the morning 
observation; it then turned to the N.E., and in the evening advanced over 
the North Sea nearly to the south of Norway, as shown by the pressure and 
direction of the winds at that time, and soon after became absorbed in Storm V. 
As the position of the centres of Storms VIII. and X. could be ascertained only 
on one day, the rate of their motion cannot be determined. 

VOL. XXIV. PART I. 3 H 



200 MR ALEX. BUCHAN ON THE STORMS OF WIND WHICH OCCURRED 

Since storms generally travel to the N.E. at an average speed of about twenty 
miles an hour, and since the distance of the S.W. of Ireland from any British 
port does not exceed 500 miles, it follows that these storms might have been pre- 
dicted at least twenty-four hours before their occurrence at the eastern seaports 
of Great Britain ; and as their approach could have been foreseen some hours 
before they burst upon the west of Ireland, they might have been predicted from 
thirty-six to forty-eight hours beforehand. 

Comparison of the Barometric and Thermometric Lines. 

The observations of the thermometer do not equal in importance those of the 
barometer, for this among other reasons, that while the barometer measures the 
weight of the whole atmosphere pressing on it, the thermometer gives only the 
temperature of that portion of the air which is in immediate contact with the 
earth. There appears to be little apparent connection between these lines at first 
sight ; for while the barometric lines approach more or less closely the curves of 
the circle or the ellipse, the lines of equal thermometric disturbance present the 
greatest possible irregularity of form. When, however, the attention is confined 
to the region of greatest barometric disturbance, a remarkable connection is at 
once observed. It will be seen that in all cases the temperature rose a few 
degrees over the space toward which and over which the front part of the storm 
was advancing, and fell at those places over which the front part of the storm 
had already passed. In other words, the temperature rose as the barometer fell, 
and fell as the barometer rose. Generally, the temperature in advance of the 
storm was above the average, and in the rear of the storm below it. But if it 
was considerably above the average in advance of the storm, it was still above 
the average when the storm had passed, though lower than it was before. 

In one or two cases the temperature, after falling a little, rose in what ap- 
peared to be the wake of a storm ; but in these cases the observations of the fol- 
lowing day showed that another storm was advancing close upon the one already 
past. The high temperature thus indicated the approach of the second storm, and 
properly belonged to it. 

Observations of Rain and Cloud, 

We learn from the observations that as long as the barometer did not fall 
below the mean, there was no continuous rain anywhere, but blue sky prevailed, 
varied with partially clouded sky or with fog. But when the barometer fell, the 
sky began to be obscured, and rain to fall at intervals ; and as the central de- 
pression advanced, the rain became more general, heavy, and continuous. After 
the centre of the storm had passed, or when the barometer had begun to rise, the 
rain generally became less heavy, falling more in showers than continuously ; the 



IN EUROPE DURING OCTOBER, NOVEMBER, AND DECEMBER 1863. 201 

clouds began to break up, and fine weather, ushered in with cold breezes, ulti- 
mately prevailed. 

In order to show where the greatest amount of rain fell, Table IV. has been 
prepared, giving the rainfall at those places over which, or near which, the 
storms passed. It is necessary to explain that, as far as known, the rain given 
in the table fell during the twenty-four hours preceding the date of each entry. 
Thus, as the centre of Storm II. was west of Ireland on the 1st November, and 
in the centre of England on the 2d, the rainfall of the 2d took place as the storm 
travelled between these places. The rainfall at the Irish, English, and French 
stations, over which the front part of the storm had passed, was excessive — two 
inches having fallen at Brest ; one inch at Liverpool and Dover ; and about three- 
quarters of an inch at L'Orient, Galway, &c. On the same day the rainfall in 
Scotland was everywhere small, none falling at many places, and the largest fall 
being about one-sixth of an inch at Portree, in Skye. In Scotland, where the fall 
of rain was small, the wind was feeble, in no case blowing a gale ; and the baro- 
meter, though low, had varied little during the twenty- four hours, and a pressure 
almost equally low prevailed for a considerable distance round. On the other 
hand, where the rainfall was in excess, violent gales prevailed, the fluctuations of 
the barometer had been great, and the isobarometric lines were much crowded 
together in the vicinity. On the following day the storm had passed eastward to 
Denmark. The rain over the west of England and of France had diminished, 
but increased over the east of England, and in Belgium and the Netherlands, over 
which the storm had travelled on its way to Denmark. The Irish rainfall was 
small, but not so small as would have been, but for the advance of Storm III., whose 
rainfall swelled the amount ; and the same cause increased the Scottish rainfall. 

All the other storms showed similar relations to the rainfall. The amount 
precipitated was greatest during the time the front part of the storm passed any 
place, and appeared to be in a great measure proportioned to the atmospheric 
disturbance experienced during the twenty-four hours, and the violence of the wind 
occasioned by that disturbance. In the wake of storms, though the atmospheric 
disturbance was equally great, and the violence of the wind as great, or even 
greater, the rainfall was very much less, except when the advance of another 
storm increased the amount. 

Observations of the Wind. 

Every one of the storms on each day presented the winds under the same 
conditions, viz., whirling round the area of low barometer in a circular manner, 
in a direction contrary to the motion of the hands of a watch, with a constant 
tendency to turn inwards towards the centre of lowest barometer. The wind 
in storms neither blows round the centre of least pressure in circles (or as tan- 
gents to the concentric barometric curves), nor does it blow directly towards that 



202 MR ALEX. BUCHAN ON THE STORMS OF WIND WHICH OCCURRED 

centre. It takes a direction nearly intermediate, approaching, however, more 
nearly the direction and course of the circular curves than of the radii to the 
centre. To this general rule none of the eleven storms any day offered an ex- 
ception. When the centre of the storm was in a situation where observations 
were made all round it, the following were the general directions as observed :— 



At p 



aces S. of the centre of least pressure, the wind was generally S.W 
S.E. „ „ „ S. 



E. 

N.E. 

N. 
N.W. 

W. 

s.w. 



S.E. 
E. 

N.E. 

N. 

N.W. 

W. 



The greater the force of the wind at any place, the more nearly did it approxi- 
mate to the directions here indicated. On those occasions when no observa- 
tions were obtained from one or more of the sides of the storm, such observations 
as were obtained followed the same rule. Hence the atmosphere on every occa- 
sion rotated round the centre of the storm ; and it should be kept in mind that 
this is no theoretical statement, but the result of observations faithfully put down 
on maps. 

It will follow from this, that as the storms advanced to the eastward the general 
veering of the wind at places lying north of the central path of the storm would 
be from the N.E. by N. to W. ; and at places to the south of the centre, from the 
N.E. by E. and S. to N.W. 

On referring to the chart of the 2d November (Plate XVI.), it will be seen 
that the violence of the wind was greatest in the north of France, and south of 
England and Ireland, where there were great differences in the pressure, as shown 
by the crowding together of the isobarometric lines. On the other hand, it will 
be seen that the wind was nowhere blowing a gale in North Britain, where the 
pressure varied little for a great distance all round, as shown by the distance 
between the isobarometric lines, even though the pressure there was absolutely 
low. Again, on the 11th November (Plate XVIIL), the isobarometric lines were 
far apart in Storm V. in the north, and the wind was nowhere strong within that 
disturbed area ; whereas the lines were much crowded in Storm VI. round Ply- 
mouth, and the wind was blowing strongly all round. This blowing of the wind 
from a high to a low barometer, and with a force generally proportioned to the 
differences of the pressure, would appear from these storms to be the most im- 
portant law concerned in regulating the movement of the wind. As the wind 
approached the centre of least pressure, its violence gradually abated, till, on reach- 
ing the centre, a lull or calm prevailed. 

Calms and light winds also prevailed along the ridge of highest barometer, or 
the region where the pressure was greatest, and on receding from which, on each 






IN EUROPE DURING OCTOBER, NOVEMBER, AND DECEMBER 1863. 203 

side, the pressure diminished. It may not unaptly be compared to the watershed 
in physical geography, since from it the winds flowed away towards those places 
where the pressure was less. It sometimes extended over the Continent from 
N. to S., sometimes from E. to W., and sometimes in other directions ; frequently 
it curved through Europe in a very irregular manner, forming the boundary line 
between a disturbed area in the north and another in the south ; occasionally it 
was broken up into different parts ; and more rarely it was concentrated in one 
locality, forming an area of high barometer approaching a circular form. In this 
last case, which happened on the 5th December in western Europe (Plate XXI.), 
and on several other occasions, the wind was always observed gently whirling 
out of the area of high barometer, in the direction of the motion of the hands of a 
watch — being the opposite direction to that assumed by the wind when it blows 
round and in towards an area of low pressure. 

Storms of the Mediterranean. 

The observations from Austria, Turkey, Greece, Russia, and Syria are too 
scanty to enable us to trace satisfactorily any , of the storms which occurred 
there during the period. There is enough, however, to show that the conclusions 
which may be drawn from those storms which passed over northern and western 
Europe cannot safely be applied to the storms of the Mediterranean, as regards 
their form, the direction from which they come, and the course generally pursued 
by them. 



App. 



VOL. xxiv. part i. 3 I 



204 



MR ALEX. BUCHAN ON THE STORMS OF WIND WHICH OCCURERD 





b- 






OS 






i— * 






. 


A 




Ph 


CM 




-t-» 


CN 




e8 


•e 
i-l 




o 

+3 


03 




a) 


S G5 
2 to 

a i 

O 00 




«*h 


H •* 






* * 




CO 


o 




CD 


a N 




00 


g ^ 






i_r ■** 






H © 




o 


2 ^ 




^2 


R* 




<U 


H ."" 






H CJ 

Ph o 




^3 


AND 




<D 


03 o 




+3 






O 5> 




o 


to s 




-M 


XI £ 




T3 


SS 


• 


<M 


X 


1— 1 


<5 r<8 


(— 1 

p 


a 


W K2 


525 


t— 1 


Barom 


Pu 


a 


M ^ 


< 


o 


r ^ 




-<-J 


P=< <u 




ID 


o ■» 




c+-i 


M O 




o 






CO 






CO 


ft s 




So 

o 


2 ! 




P4 


> 




<D 

.4 


H CO 




-t-s 




be 




P 


Ph fi. 






u_ CM 




fe 


«« CM 




p- 


O _ 




O 


O co 




co 


CjS & 




co 


fc a 




o 


1-1 P5 






O p£J 






CO w 




1 p 




CD 
CO 


HH g 




rO 


E-i 




O 


H 




,__! 


H- 1 




CJ 


pq 




o 


<1 




-+■3 


EH 




• P-* 






-3 






T3 






<3 







jq 


















03 

bo 


o 


CO 


o 


* ffi (M (O i- iiOoiCOiO 


CO o 










_C 




a^ 


CO 


cocoascsoooi— i i— < 


I-H <N 










-3 


© 


— C5 




o 












c3 


o 


CN 




CO 












o 


» 
















































m 




















CD 


»d 


CO 


■* 


ffl'*CO'H^NH(M'# 


CO CO 










a 


^ 


J*> 


CO 














o 




S& 




o 












c3 

pq 


O 


<M 




CO 












13 










J o 


I— 1 


(MCOTiMxOCOt^COC»0 


r-l <N 

CN CN 

CO 










. ^ . 

CO ci ;-. 

ops 


d M 














co M o 


















rt ^"W 


t> 






d 












0J 






CJ 










"8 

o 


fi 






ft 










fcH 


















S 




















j 










OQ 

to 


[3 


O 


Jt- 


«o-*conNMoco 


t-- CO 










_a 


'? 


. Oi 


03 


cpOr-ii-iCNCMCOrJ(r}( 


»o co 










aS 




CD 


•~ CO 




en 




"o 








cd 


<D 


CM 




<M 










K 


6 










'& 








o 












a 






























CJ 








t* 












CJ 








a 

o 

pq 


"~P 


C7> 


l> 


tlOnNMON^W 


CN O 


M 








| 


• = CO 


OS 


O O i-< i— ICMCMCO-*»0 


co j>- 


"o 






O 


CM 




CM 






a 


















.S c2 


CJ 
CJ 


























"■§ X 


M 














S o 


o 






c3 


■ <—l 


CM 


eooi-<CMTj<coiocot^' 


co a> 


QJ ^^ 








. >> . 


•O (M 


CM 


CN 




s rt 

a > 

"S a 

3 


e3 






1863 

Month, Da 

Hour 


ci 

0J 

ft 




CO 

6 

9 

ft 


co 

CJ 

ft 


CJ 

3 

> 

a 

3 


eg 


4 

$ 

a 

CJ 
CJ 












co S 

CM - R 


a 


o 


o 




rO 












■4J 

c3 


CO 


.H 


CO 


CO 


t»(D«3IMffl^©NlO 


CO CT> 


•o rt 


c3 






o 


o 

CD 


. co 

CM 


co 


eococoeocNi-ioojco 

CO 
CN 


CO jT^ 


^ a 

-3 «« 


a 




0? 

3 




C5 










o § 


u 
C3 

c 
o 


a 



e 


a 

3 

a 




.— I 


o 


COt^TjHOTHCOOCOCO 


•^ o 


a 

o 


H 

O 


C ? 

"*" C7i 
CM 


CO 


cNCNcNrioa>coir-<x> 

CO 
CN 


|> CO 


c3 rt 
be « 
.S E 

T3 O 
c3 Tjt 
CJ 


H-3 


E 

'a 


3 

'a 












o 


IQ 


CN 


p^ 










CN 


^ 


I— < 


fl 






i-(t» «H< 




M ,J- 








. 1^ . 


_• © 


I— 1 


hNWt)iOON0503 


C5S O 


s 2 
Is 

a g 


I— 1 
I— 1 


CO 
1 — 1 


o 

CN 










1863. 

li, Da 
Hour 


^•<M 
ci 






CN 


o 

H-3 


o 


o 


"3 

o 


ft 






ft 


■a o 

fa TlH 


o 

co 


o 

CO 


o 

CO 


H 










CM CO 
CN 


05 


co 
1—1 


I— 1 
















^ 










■3 73 








CO 

to 


o 


CM 


.— 1 


■Hl^t^ioCO^MNO 


Ttl CO 


i-i CN 


CN 


<N 


CN 


C 


Pi 


««= 


CO 


COCOCOoOrHCMCMCO 


00 CO 


d 










o 


■- co 




C5 




CJ 












CM 




CN 




ft 










O 




























'rj 




















(0 


rd 


t^ 


CO 


rf^io^oro^oco 


1—1 1— 1 










3 


M 


.t^ 


I> 


COCOCnOr-Hr-iCNCNCN 


CO CO 










o 




.2 co 




Oi 












c3 

PQ 


O 


<M 




CM 




















Hes 


^Ei 


• CM 


CO 


Oi-iCNCOr}<kOCOi>CO 


C5 O 










-=> CM 


CM 
















d*- 1 




CN 


CM 










CO ^3 

^ g'fl 


o 




ci 


ci 










a> 




a> 


CJ 










g 53 


ft 




ft 


ft 











IN EUROPE DURING OCTOBER, NOVEMBER, AND DECEMBER 1863. 205 





Ph' 
OS 


O 


CO 


tJ< © 


t^ 


»o 












CM 


»o 


CO 


© 


© 


tH 


o 


o ra to 


© 


© 




TH 


■<# 


CO j> 


CO 


r-l 


" 


• 


* 




" 


lO 


»o 


© 


CM 


CM 


CO 


TO 


• — ' CO T— 1 


o 


TO 




© 








o 


























© o 








CM 








CO 


























CM TO 






a 










o 


CM 










CM 






















• 


• 


" 




CM 


CM 






























CO 


Pi 


• 


• 


• 


• 


o 




• 


• 


• 


• 




• 


. 


. 


• 


. 


. 


: : : 


'. 


: 


CD 


CD 










CO 
































CO 












































u 


a 










T* 


»G> 


o 






lO 


© 




© 


CM 


»o 


•HH 










p£a 


• 


• 


• • 


• 


CM 


CM 


CM 


• 


l 


T*l 


^< 


; 


rjH 


CM 


T-l 


TO 


• 


• 


• 


• 


a 












O 






• 


' 






• 


















CD 


eo 










CO 
































O 












































B 


H 

o 










CO 


© 










© 


© 


















,a 










CN 


CO 


• 


• 


• 


; 


^ 


© 


















■* 


o 










o 
co 




















" 


* 


" 


* • • 


• 




4 


CM 


CO 


CM lO 


CO 


^* 


*o 








© 


TH 


CM 


© 


M 


© 


CM 


TO 


CO TO i— 1 


(Ti 


i— i 




CO 


CO 


CO © 


o 


CM 


CM 


■ 


■ 




© 


^f 


© 


CM 


i—l 


© 


CM 


t^ 


i— c lO t- 


© 


© 




© 






o 








■ 






© 








© 


© 


© 












CM 






CO 














© 








CM 


TO 


CN 




















CM 


© 










o 






















r& 2 


• 


• 


• 


• 


o 


os 


• 


• 


• 


• 


I— 1 


• 


• 


• 


• 


• 


• 


. 


• 






^ 










o 


© 
































" fl 










CO 


CM 










© 




















a 


eo 


CO 


CM © 


o 


T!H 






© 


CO 




© 


i— 1 


CM 


^H 


r^ 




U3 


N O O 


»o 


■* 




CM 


CM 


lO lO 


t^ 


CO 


• 


" 


i— i 


i—i 


• 


© 


© 


"tf 


TO 


r~ 


• 


i—l 


I-H I-H © 


>o 


CO 




Ph 


© 










• 


• 


o 




• 


© 








© 




OS 








co 


05 


CM 














CO 






CM 








CM 




CM 


















CO 


CO 




T-l 


© 




co 




















oo 


a 




• 




• 


lO 

OS 


■* 


: 


1— 1 
© 


© 




© 
© 




















a 


CD 










CM 






CO 






CM 




















g 










o 


© 


CM 


I—l 


© 


ra 


»o 




lO 


© 


iO 


© 










o 


; 


• 


• 




co 


CM 


i—l 


© 


© 


© 


© 


• 


CM 


rH 


ra 


© 


• 


• 




• 


B 


Ph 










OS 






© 


© 












© 


© 










n 


co 










CM 






CO 


CM 












CM 


CM 












o 
o 










o 

1—1 

OS 
CM 


© 

© 


: 


OS 
CO 


© 


: 
























r^ 


© 


■* O 


CO 


T— 1 


co 




o 


© 


lO 


lO 


»o 


lO 


tH 


Tf< 


CO 


Tfl 


© i> m 


TO 


TO 




g 


© 


© 


© OS 


t~ 


OS 


co 




t-» 


© 


CM 


^ 


lO 


CN 


CM 


TO 


CM 


»o 


to © ra 


ra 


O 




< 


00 












• 


© 
























© 




C5 


CM 














CM 
























CO 














t^ 


i— i 




© 


© 




CM 






















n3 S 










CO 


Th 


* 


© 


© 




ra 






















sH-5? 










os 




• 






• 
























" a 










CM 


































CO 


CO 


m t~- 


co 


CO 






© 


O 




tH 


ra 


« 


lO 


>* 


TO 


TO 


t^ t# © 


rH 


CM 




b 


co 


O 


O rH 


CN 


•* 


; 


• 


oo 


© 


• 


J> 


lO 


© 


CM 


CM 


CM 


TO 


TOO© 


l> 


ra 




CM 


CO 


© 








• 


• 


© 




• 


© 




















CO 

CO 


OS 


CM 


CM 












CM 






CM 






























^ 


.— i 




co 


CM 




M 




















oo 


S 










CO 


tH 


• 


1^- 


© 


* 


iO 




















1-1 


Ph 










c* 




• 


CO 






© 




















03 

a 


to 










CM 






CM 






CM 






























M< 


O 


© 


tH 


00 


© 


OS 




© 


© 


© 


TO 










o 


a 




• 


• 


• 


CM 


i— ( 


© 


O 


CM 


"* 


CM 


• 


i—l 


CM 


CM 


i—l 


; 


' • '. 


; 


; 


B 


Ch 




• 


• 




os 














• 










• 


• . 


• 


• 


CN 


CO 










CM 






















































































ia 


tH 




1^ 


© 




CM 


»o 




















o 










© 


© 


• 


CM 


CO 


* 


CM 


© 




















o 


• 


• 






OS 


CO 


• 


© 




• 
































CM 


CM 




CM 




























rfi 


co 


t~- CO 


os 


"tf 


O 




,_, 


TH 


*^ 


© 


o 


^ 


TO 


T* 


tH 


t^ 


O 00 © 


CO 


© 




s 


CO 


o 


I— 1 I—I 


o 


o 


© 


• 


co 


co 


© 


© 


ra 


© 


^ 


lO 


TH 


I> 


co ra cm 


© 


i— i 




< 


© 










© 


• 






© 


© 














© 








CO 


CM 










CM 








CM 


CM 














TO 








*<3 

m 
C3 


es 
O 

a 

o 
02 


o 

CO * 


a" 

CD 

O 


F o 
o 

Oh 

^H 

CD 

> 

13 


a" 

# C 

'-C 
-ij 
o 


-*j 

to 
c3 
O 

u 
"o 
J> 

<v 
pq 


T3" 

S-l 

O 


cs 

d 

CO 

a> 


a 

O 

eg 

i— ( 

O 


c3 

Ph 


a 

CO 




a 


o 

CJ 
-H^> 


a 

CP 

'O 

tH 

c3 
& 

CO 
<D 


to 

-^ 
0) 
O 

w 


a 
u 

O 

£ 
Ph 


<£ go 
. .2 -S 


3~ 

C3 

ID 

<x> 
u 

PQ 


u 

CJ 

-i^> 

a 
p 

a 

to 

a 

CJ 

M 



( 207 ) 



XVII. — On the Celtic Topography of Scotland, and the Dialectic Differences 
indicated by it. By W. F. Skene, Esq. 

(Read 17th April I860.) 

The etymology of the names of places in a country is either a very important 
element in fixing the ethnology of its inhabitants, or it is a snare and a delusion, 
just according as the subject is treated. When such names are analysed accord- 
ing to fixed laws, based upon sound philological principles, and a comprehensive 
observation of facts, they afford results both important and trustworthy ; but if 
treated empirically, and based upon resemblance of sounds alone, they become a 
mere field for wild conjectures and fanciful etymologies, leading to no certain 
results. The latter is the ordinary process to which they are subjected. The 
natural tendency of the human mind is to a mere phonetic etymology of names, 
both of persons and of places. It is this tendency which has given rise to what 
may be called punning etymologies, in which the King of Scotland plays so 
facetious a part, when the first Guthrie had that name fixed upon by the king, 
from his proposing when asked, how many fish should be prepared, to gut three ; 
and when Rosemarkie received its name because the king, on asking what land 
he neared, was answered, Ross mark ye. This illustrates the natural tendency to 
suggest a mere phonetic etymology, in which the sounds of the name of the place 
appear to resemble the sounds in certain words of a certain language, the 
language from which the etymology is derived being selected upon no sound 
philological grounds, but from arbitrary considerations merely. 

Unhappily, an etymology founded upon mere resemblance of sounds has 
hitherto characterised all systematic attempts to analyse the topography of Scot- 
land, and to deduce ethnologic results from it. Prior to the publication of the 
" Statistical Account of Scotland" in 1792, it may be said that no general attempt 
had been made to explain the meaning of the names of places in Scotland, or 
to indicate the language from which they were derived. We find occasionally, 
in old lives of the saints, and in charters connected with church lands, that names 
of places occurring in them are explained ; and these interpretations are very 
valuable, as indicating what may be termed the common tradition of their mean- 
ing and derivation at an early period. Of very different value are a few similar 
derivations in the fabulous histories of Boece, Buchanan, and John Major, 
which are usually mere fanciful conjectures of pedantry. 

The first impetus to anything like a general etymologising of Scottish topo- 
graphy was given when Sir John Sinclair projected the " Statistical Account of 
vol. xxiv. part i. 3 k 



208 MR W. F. SKENE ON THE CELTIC TOPOGRAPHY OF SCOTLAND 



Scotland." In the schedule of questions which he issued in 1790 to the clergy of 
the Church of Scotland, the first two questions were as follows : — 

1. What is the ancient and modern name of the parish ? 

2. What is the origin and etymology of the name ? 

This set every minister thinking what was the meaning of the name of his 
parish. The publication of the " Poems of Ossian," and the controversy which 
followed, had tended greatly to identify national feeling and the history of the 
country with Gaelic literature and language, and, with few exceptions, the 
etymology was sought for in that language. The usual formula of reply was, 
" the name of this parish is derived from the Gaelic," and then followed a Gaelic 
sentence resembling in sound the name of the parish, and supposed admirably to 
express its characteristics, though the unfortunate minister is often obliged to 
confess that the parish is remarkably free from the characteristics expressed by 
the Gaelic derivation of its name. These etymologies are usually suggested irre- 
spective entirely of any known facts as to the history or population of the parish, 
and are purely phonetic. 

Thus the writer of the account of Elie, in the New Statistical, observes : — 
" The writer of the former Statistical Account has, according to the fashion 
which seems to have prevailed in his day, as well as now, had recourse to Gaelic, 
the mother as it should seem of languages, and tells us that the parish received 
its name from ' A Liche,' signifying ' out of the sea.' We are disposed to doubt its 
soundness, for the village is not further out of the sea than any other part of the 
coast, nay, it extends further into it. We should rather be inclined to consider 
Elie as having sprung from the Greek word elos, a marsh." 

Both etymologies are entirely irrespective of the fact, that the old form of the 
word was " chellm.'' 

After the publication of the Statistical Account, Gaelic was in the ascendant 
as the source of all Scottish etymologies, till the publication of Chalmers' 
" Caledonia" in 1807. John Pinkerton had indeed tried to direct the current of 
popular etymology into a Teutonic channel, but his attempts to find a meaning 
in Gothic dialects for words plainly Celtic were so unsuccessful, that he failed 
even to gain a hearing. Chalmers was more fortunate. His theory was, that 
a large proportion of the names of places in Scotland are to be derived from the 
Welsh, and indicate an original Welsh population. And this he has worked out 
with much labour and pains. In doing so, he was the first to attempt to show 
evidence of the dialectic difference between Welsh and Gaelic pervading the names 
of places, and to discriminate between them ; but for almost all the names of 
places in the Lowlands of Scotland he furnishes a Welsh etymology, which, like 
his predecessors the Scottish clergy, he supposes to be expressive of the charac- 
teristics of the locality. His theory has, in the main, commanded the assent of 
subsequent writers, and is usually assumed to be, on the whole, a correct repre- 
sentation of the state of the fact. Yet his system was as purely one of a phonetic 



AND THE DIALECTIC DIFFERENCES INDICATED BY IT. 209 

etymology, founded upon mere resemblance of sounds, as those of his predecessors. 
The MSS. left by George Chalmers show how he set about preparing his etymo- 
logies, and we now know the process he went through. He had himself no 
knowledge of either branch of the Celtic language, but he sent his list of names to 
Dr Owen Pughe ; and that most ingenious of all Welsh lexicographers, who was 
capable of reducing every word in every known language in the world to a Welsh 
original, sent him a list of Welsh renderings of each word, varying from twelve to 
eighteen in number, out of which Chalmers selected the one which seemed to 
him most promising. 

As an instance, we may refer to a pet etymology of Chalmers, on which he 
has built as historical fact, and which has been followed by all subsequent writers. 
He interprets Kilspindy, the name of a place in Aberlady Bay, which belonged 
to the bishop of Dunkeld, as signifying in Welsh CM ys pendu, which he renders 
"the Cell of the Black Heads," and supposed that it indicated a settlement of 
the Culdees. We have no reason to suppose that the Culdees were distinguished 
by having black head-dresses ; but the etymology is philologically false, for Cill 
is Gaelic and not Welsh. Ys is no known form of the article in Welsh, and 
pen du means black head in the singular. In the plural, it would be penau 
duon. The old form of the word puts the etymology to rout, for it was originally 
written " Kinespinedin." His other etymologies are equally founded on a mere 
resemblance of sounds between the modern form of the word and the modern 
Welsh, as those of the clergy in the Statistical Account were between the modern 
form of the word and the modern Gaelic. 

That system of interpreting the names of places, which I have called phonetic 
etymology, is, however, utterly unsound. It can lead only to fanciful renderings, 
and is incapable of yielding any results that are either certain or important. 

Names of places are, in fact, sentences or combinations of words originally 
expressive of the characteristics of the place named, and applied to it by the 
people who then occupied the country, in the language spoken by them at the 
time, and are necessarily subject to the same philological laws which governed 
that spoken language. The same rules must be applied in interpreting a local 
name as in rendering a sentence of the language. 

That system, therefore, of phonetic etymology which seeks for the interpre- 
tation of a name in mere resemblance of sound to words in an existing language, 
overlooks entirely the fact that such names were fixed to certain localities at a 
much earlier period, when the language spoken by those who applied the name 
must have differed greatly from any spoken language of the present day. 

Since the local names were deposited in the country, the language itself from 
which they were derived has gone through a process of change, corruption, and 
decay. Words have altered their forms — sounds have varied— forms have become 
obsolete, and new forms have arisen — and the language in its present state no 
longer represents that form of it which existed when the local nomenclature 



210 MR W. F. SKENE ON THE CELTIC TOPOGRAPHY OF SCOTLAND, 

was formed. The topographical expressions, too, go through a process of change 
and corruption till they diverge still further from the spoken form of the language 
as it now exists. 

This process of change and corruption in the local names varies according to 
the change in the population. When the population has remained unchanged, 
and the language in which the names were applied is still the spoken language 
of the district, the names either remain in their original shape, in which case they 
represent an older form of the same language, or else they undergo a change 
analogous to that of the spoken language. Obsolete names disappear as obsolete 
words drop out of the language, and are replaced by more modern vocables. 
Where there has been a change in the population, and the older race are replaced 
by a people speaking a kindred dialect, the names of places are subjected to the 
dialectic change which characterises the language. There are some striking 
instances of this where a British form has been superseded by a Gaelic form, as, 
for instance, Kirkintulloch, the old name of which, Nennius informs us, was 
Cserpentaloch, kin being the Gaelic equivalent of the Welsh pen ; Penicuik, the 
old name of which was Penjacop ; Kincaid, the old name of which was Pencoed. 

When, however, the new language introduced by the change of population is 
one of a different family entirely, then the old name is stereotyped in the shape in 
which it was when the one language superseded the other, becomes unintelligible 
to the people, and undergoes a process of change and corruption of a purely 
phonetic character, which often entirely alters the aspect of the name. In the 
former cases it is chiefly necessary to apply the philologic laws of the language to 
its analysis. In the latter, which is the case with the Celtic topography of the 
low country, it is necessary, before attempting to analyse the name, to ascertain 
its most ancient form, which often differs greatly from its more modern aspect. 

It is with this class of names we have mainly to do, as presenting the pheno- 
mena I am anxious to investigate. 

When the topography of a country is examined, its local names will be found, 
as a general rule, to consist of what may be called generic terms and specific 
terms. What I mean by generic terms are those parts of the name which are 
common to a large number of them, and are descriptive of the general character 
of the place named ; and by specific terms, those other parts of the name which 
have been added to distinguish one place from another. The generic terms are 
usually general words for river, mountain, valley, plain, &c. ; the specific terms, 
those words added to distinguish one river or mountain from another. Thus, in 
the Gaelic name Glenmore, glen is the generic term, and is found in a numerous 
class of words — more, great, the specific, a distinguishing term, to distinguish 
it from another called Glenbeg. In the Saxon term Oakfield, field is the generic 
term, and oak the specific, to distinguish it from Broomfield, &c. 

When the names of places are applied to purely natural objects, such as 
rivers, mountains, &c, which remain unchanged by the hand of man, the names 



AND THE DIALECTIC DIFFERENCES INDICATED BY IT. 211 

applied by the original inhabitants are usually adopted by their successors, though 
speaking a different language ; but the generic term frequently undergoes a pho- 
netic corruption, as in the Lowlands, where Aber has in many cases become Ar in 
Arbroath, Arbuthnot ; Ballin has become Ban, as in Bandoch ; Pettin has become 
Pen as Pendriech ; Pol has become Pow ; and Traver has become Tar and Tra. 

On the other hand, where the districts have been occupied by different 
branches of the same race, speaking different dialects, the generic terms exhibit 
the dialectic differences when the sounds of the word are such as to require the 
dialectic change ; thus in Welsh and Gaelic : — 

Pen and Kin — a head, 
Gwyn and Fionn — white, 
shows the phonetic difference between these dialects. 

The comparison of the generic terms which pervade the topography of a 
country affords a very important means of indicating the race of its early inhabi- 
tants, and discriminating between the different branches of the race to which the 
respective portions of it belong. 

Between the Celtic and Teutonic races the generic terms afford this great 
leading distinction, that in Celtic names they are invariably found at the begin- 
ning of the word ; in Teutonic names, at the end of the word. Thus, Glenesk in 
Celtic is Eskdale in Teutonic; Dunedin is Edinburgh; Auchindarroch is Oak- 
field, and so forth. In the one, the generic term, at the beginning of the word ; 
in the other, at the end. 

It was early observed that there existed in the Celtic generic terms a difference 
which seemed to indicate dialectic distinction. Even in the Old Statistical 
Account, the minister of the parish of Kirkcaldy remarks, — " To the Gaelic lan- 
guage a great proportion of the names of places in the neighbourhood, and 
indeed through the whole of Fife, may unquestionably be traced. All names of 
places beginning with Bal, Col or Cul, Dal, Drum, Dun, Inch, Inver, Auchter, 
Kil, Kin, Glen, Mon, and Strath, are of Gaelic origin. Those beginning with 
Aber and Pit are supposed to be Pictish names, and do not occur beyond the 
territory which the Picts are thought to have inhabited." 

Chalmers states it still more broadly and minutely. He says, — " Of those 
words which form the chief compounds in many of the Celtic names of places in 
the Lowlands, some are exclusively British, as Aber, Llan, Caer, Pen, Cors, and 
others ; some are common to both British and Irish, as Cam, Craig, Crom, Bre, 
Dal, Eaglis, Glas, Inis, Rinn, Ros, Strath, Tor, Tom, Glen ; and many more are 
significant only in the Scoto-Irish or Gaelic, as Ach, Aid, Ard, Aird, Auchter, 
Bar, Blair, Ben, Bog, Clach, Corry, Cul, Dun, Drum, Fin, Glac, Inver, Kin, Kil, 
Knoc, Larg, Lurg, Lag, Logie, Lead, Letter, Lon, Loch, Meal, Pit, Pol, Stron, 
Tullach, Tullie, and others. , ' 

This attempt at classification is, however, exceedingly inaccurate. Two of 
the words in the first class, Llan and Caer, are common to both British and Irish ; 

VOL. XXIV. PART I. 3 L 



212 MR W. F. SKENE ON THE CELTIC TOPOGRAPHY OF SCOTLAND, 

and a large portion of the third class are significant in pure Irish, as well as in the 
Scoto-Irish or Gaelic. No attempt is made to show, by the geographical distribu- 
tion of these words, in what parts of the country the respective elements prevail. 

In a recent work, however, of some pretension, by an eminent Gaelic scholar, 
this attempt is made ; and I refer to it to show how very loosely popular ideas 
on this subject are taken up. He says, " The Blackadder and Whiteadder con- 
tain distinctly the British Dwfr or Dwr, water." The two names are Teutonic, 
and have obviously no Celtic form. " In East Lothian, Yester is the old British 
word Ystrad, a valley." This is correct, but it is on British ground. " Tranent 
and Traquair have the British Tre, a town." The old form is Travernent and 
Traverquair, and Traver is unknown in Welsh topography. " On crossing the 
Forth, British names still appear nowhere more clearly than in the name of the 
Ochil Hills, where the British Uchel (high), cannot be mistaken." This is phonetic 
etymology, and, as we shall see, it has been mistaken. " In Fife we find several 
Abers, Pits, and Pittens, indicating the existence of a British population ; and 
again the Pits and Pittens of Forfarshire are numerous." Of the Abers we shall talk 
presently ; but if the Pits and Pittens indicate a British population, how comes it 
that they are unknown in Wales, and are not to be found in Welsh topography. 
" We have," says he, " Pens and Abers and Pits in abundance on through Kin- 
cardine and Aberdeenshire." Abers and Pits certainly, but no Pens except one 
solitary instance, which is doubtful. I need not proceed. The statement goes on 
in the same strain, at equal variance with topographical and philological facts. 

The most popular view of the subject, and that which has recently been most 
insisted in, is the line of demarcation between a Kymric and a Gaelic population, 
supposed to be indicated by the occurrence of the words Aber and Inver. 

This view has been urged with great force by Kemble, in his Anglo-Saxons ; 
but I may quote the recent work by Mr Isaac Taylor, on words and places, as 
containing a fair statement of the popular view of the subject : — 

" To establish the point that the Picts or the nation, whatever was its name, 
that held central Scotland, was Cymric, not Gaelic, we may refer to the distinc- 
tion already mentioned between Ben and Pen. Ben is confined to the west and 
north ; Pen to the east and south. Inver and Aber are also useful test w T ords in 
discriminating between the two branches of the Celts. The difference between 
the two words is dialectic only ; the etymology and the meaning is the same — a 
confluence of waters, either of two rivers or of a river with the sea. Aber occurs 
repeatedly in Brittany, and is found in about fifty Welsh names, as Aberdare, 
Abergavenny, Abergele, Aberystwith, and Barmouth, a corruption of Abermaw. 
In England we find Aberford in Yorkshire, and Berwick in Northumberland and 
Sussex ; and it has been thought that the name of the Humber is a corruption of 
the same root. Inver, the Erse and Gaelic forms, is common in Ireland, where 
Aber is unknown. Thus, we find places called Inver in Antrim, Donegal, Mayo, 
and Invermore in Gal way and in Mayo. In Scotland the Invers and Abers 



AND THE DIALECTIC DIFFERENCES INDICATED BY IT. 213 

are distributed in a curious and instructive manner. If we draw a line across 
the map from a point a little south of Inveraray to one a little north of Aberdeen, 
we shall find that (with very few exceptions) the Invers lie to the north of the 
line and the Abers to the south of it. This line nearly coincides with the present 
southern limit of the Gaelic tongue, and probably also with the ancient division 
between the Picts and the Scots." 

Nothing can be more inaccurate than this statement. Ben is by no means 
confined to the west and north ; and as examples of Pen, he refers, among others, 
to the Pentland Hills, Pentland being a Saxon word, and corrupted from Pectland ; 
and to Pendriech in Perthshire, which is a corruption from Pettindriech. 

So far from Inver being common in Ireland, it is very rare. The Index 
locorum of the Annals of the Four Masters shows only six instances. On the 
other hand, Aber is not unknown in Ireland. It certainly existed formerly, to 
some extent, in the north of Ireland ; and Dr Reeves produces four instances 
near Ballyshannon. 

The statement with regard to the distribution of Aber and Inver in Scotland 
here is, that there is a line of demarcation which separates the two words — that, 
with few exceptions, there is nothing but Invers on one side of this line, nothing 
but Abers on the other; and that this line extends from a point a little south of 
Inveraray to a point a little north of Aberdeen. This is the mode in which the 
distribution of these two words is usually represented ; but nothing can be more 
perfectly at variance with the real state of the case. South of this line there are 
as many Invers as Abers. In Perthshire, south of the Highland line, there are 
nine Abers and eight Invers ; in Fifeshire, four Abers and nine Invers ; in Forfar, 
eight Abers and eight Invers ; in Aberdeenshire, thirteen Abers and twenty-six 
Invers. Again, on the north side of this supposed line of demarcation, where 
it is said that Invers alone should be found, there are twelve Abers, extending 
across to the west coast, till they terminate with Abercrossan, now Applecross, 
in Ross-shire. In Argyleshire alone there are no Abers. The true picture of the 
distribution of these two words is — in Argyllshire, Invers alone ; in Inverness 
and Ross shires, Invers and Abers in the proportion of three to one and two 
to one ; and on the south side of the supposed line, Abers and Invers in about 
equal proportions. 

Again he says, quoting Chalmers, " The process of change is shown by an 
old charter, in which King David grants to the monks of May, ' Inverin qui 
fuit Aberin.' So Abernethy became Invernethy, although the old name is now 
restored." In order to produce the antithesis of Inverin and Aberin, one letter 
in this charter has been altered. The charter is a grant of " Petneweme et Inverin 
quae fuit Averin ; " and I have the authority of the first charter antiquary in 
Scotland for saying that this construction is impossible ; quae fuit does not, in 
charter Latin, mean " which was," but " which belonged to," and Averin was 
the name of the previous proprietor of the lands. Abernethy and Invernethy 



214 MR W. F. SKENE ON THE CELTIC TOPOGRAPHY OF SCOTLAND 



are not the same place, and the former never lost its name. Invernethy is at 
the junction of the Nethy with the Earn, and Abernethy is a mile further up 
the river. 

When we examine these Abers and Invers more closely, we find that in some 
parts of the country they appear to alternate, as in Fife — Inverkeithing, Aber- 
dour, Inveryne, Abercrombie, Inverlevin, and so forth. 2d, That some of the Invers 
and Abers have the same specific terms attached to them, as Abernethy and Inver- 
nethy, Aberuchill and Inveruchil, Abercrumbye and Invercrumbye, Abergeldie and 
Invergeldy ; and, 3d, That the Invers are always at the mouth of the river, 
close to its junction with another river, or with the sea ; and the Abers usually 
a little distance up the river where there is a ford. Thus, Invernethy is at the 
mouth of the Nethy ; Abernethy a mile or two above. These and other facts 
lead to the conclusion that they are part of the same nomenclature, and belong 
to the same period and to the same people. 

When we look to the south of the Forth, however, we find this remarkable 
circumstance, that in Ayrshire, Renfrew, and Lanarkshire, which formed the 
possessions of the Strathclyde Britons, and was occupied by a British people 
till as late a period as the more northern districts were occupied by the Picts, 
there are no Abers at all. 

What we have, therefore, is the Scots of Argyle with nothing but Invers, 
the Picts with Abers and Invers together, and the Strathclyde Britons with 
no Abers. As a mark of discrimination between races this criterion plainly 
breaks down, and the words themselves contain no sounds which, from the 
different phonetic laws of the languages, could afford an indication of a dialectic 
difference. The truth is, that there were three words expressive of the junc- 
tion of one stream with another, and all formed from an old Celtic word, 
Ber, signifying water. These were Aber, Inver, and Conber (pronounced in 
Welsh cummer, in Gaelic cumber.) These three words were originally common 
to both branches of the Celtic as derivations from one common word. In old 
Welsh poems we find not only Aber as a living word in Welsh, but Ynver like- 
wise,* and Dr Reeves notices an Irish document in which Applecross or Appur- 
crossan is called Conber Crossan. Ynver, however, became obsolete in Welsh, 
just as Cummer or Cumber and Aber became obsolete in Irish ; but we have 
no reason to know that it did so in Pictish. In the Pictish districts, therefore, 
the Abers and Invers were deposited when both were living words in the lan- 
guage. When the Scots settled in Argyle, Aber had become obsolete in their 
language, and Inver was alone deposited, and in Strathclyde both words seem 
to have gone into desuetude. 

In the same manner Dwfr or Dwr is quoted as a word for water, pecu- 
liar to the Welsh form of Celtic, and an invariable mark of the presence of a 

* Ynver occurs twice in the Book of Taliessin. 



AND THE DIALECTIC DIFFERENCES INDICATED BY IT. 215 

British people, but the old form of this word in Scotland was Doboir, as appears 
from the Book of Deer, where Aberdour is written Abber-doboir, and in 
Cormac's Glossary of the old Irish, Doboir is given as an old Irish word for water. 
In another old Irish glossary we have this couplet : — 

" Bior and An and Dobar, 
The three names of the water of the world." 

These words, therefore, form no criterion of difference of race, and to judge by 
them is to fall into the mistake of the phonetic etymologists, viz., to apply to old 
names, as the key, the present spoken language, which does not contain words 
which yet existed in it in its older form. 

In order to make generic terms a test of dialect they must be words which 
contain sounds affected differently by the different phonetic laws of such dialects, 
— such as Pen, Gwastad, Gwern, and Gwydd, which all enter copiously into 
Welsh topography, and the equivalents of which in the Gaelic dialects are Ken, 
Fearn, and Fiodh — Gwastad having no equivalent. 

Such generic terms afford a test by which we can at once determine whether 
the Celtic topography of a country partakes most of the Kymric or the Gaelic 
character. The earliest collection of names in North Britain is to be found in 
Ptolemy's Geography in the second century, but we know too little of the 
origin of his names, whether they were native terms, or names applied by the 
invaders, to obtain from them any certain result. After Ptolemy, the largest col- 
lection of names in Great Britain is in the work of the anonymous geographer of 
Ravenna, a work of the seventh century. The exact localities are not given, but 
the names are grouped according to the part of Britain to which they belong. 
Those which commence the topography of Scotland are placed under this title :— 
" Iterum sunt civitates in ipsa Britannia quae recto tramite de una parte in 
alia id est de oceano in oceano existunt, ac dividunt in tertia portione ipsam 
Britanniam." They commence with the stations on the Roman wall between the 
Tyne and the Solway, and then proceed northwards. Among these we find two 
names together, Tadoriton and Maporiton, and as Tad and Map are Kymric 
forms for father and son, we have no doubt that here we are on the traces of 
a Kymric population. The next group is arranged under this head :— " Iterum 
sunt civitates in ipsa Britannia, recto tramite una alteri conexse, ubi et ipsa Bri- 
tannia plus angustissima, de oceano in oceano esse dinoscitur." This part of 
Britain, which is plus angustissima, is the isthmus between the Forth and the 
Clyde, and in proceeding with the names northwards we come to one called 
Cindocellum. The Ocelli Montes were the Ochills, and here the Gaelic form of 
Kin is equally unmistakeable. 

In the twelfth century, the Chartularies have preserved charters which contain 

the names of places, accompanied by an interpretation of the meaning of them. 

' One bears upon the topography of Moray. It is a charter by Alexander II. to the 

VOL. XXIV. PART. I. 3 M 



216 MR W. F. SKENE ON THE CELTIC TOPOGRAPHY OF SCOTLAND, 

monks of Kinloss of the lands of Burgyn, now Burgy, and has attached to it an old 
interpretation. Rune Pictorum is glossed the Pechts' fields, and Raoin is Gaelic 
for field. Tuber na crumkel, ane well with ane thrawn mouth — Tobar is well in 
Gaelic; Crom, crooked ; and Beul, for which Kell is probably written by mistake, 
is mouth. Tuber na fein — of the Grett or Kempis men called Fenis, ane well. 

In a perambulation of the marches of Monymusk by Malcolm IV., we have 
several such interpretations. Coritobrich is glossed Vallis fontis— Corre is 
Gaelic for valley, and Tobar, well. Scleuemingorn, Mora caprarum — Sliabh, 
Gaelic for moor ; and Gabbar, goat. Aide clothi, rivulus petrosus — Ault, Gaelic 
for a stream ; Clachach, stony. Breacachach, campus distinctis coloribus — 
Breacach, striped ; Ach, field. 

In a perambulation of the marches of Kingoldrum in 1256, we have names 
which are also glossed in a subsequent charter. Invercrumbyn is said to be the 
Concursus duorum amnium, Melgour et Crumbyn. Monybrech, Murrais of the 
quhilk runs ane strype — Monadh, a moss ; Breac, striped. Pool of Monbuy, 
yellow pool — Buidh, yellow. Athyncroich, Gallow burne, from Aid, burn ; 
Croich, gallows. 

Thus on three points in the north-eastern lowlands, in Morayshire, in Aber- 
deenshire, and in Forfarshire, we find, as early as the thirteenth century, the 
local names interpreted in Gaelic. The names themselves are, too, in the Scotch 
Gaelic, not in the Irish form, and in most cases we find the dental substituted for 
the guttural, as clothi for clachach. When we apply to the present topography the 
testing words Pen, Gwynn, and Gwydd, the Gaelic equivalents of which are Kin, 
Fearn, and Fiodh, we find that with one exception, Pen, though frequent south of 
the Forth, where there was a British population, does not occur north of the 
Forth, while it is full of Kins, and Gwern and Gwydd occur only in their Gaelic 
equivalents. 

Such then being the aspect in which the question really presents itself, it be- 
comes important, with a view to ethnological results, to ascertain more closely 
the geographical distribution of the generic terms over Scotland, and in order to 
show this I have prepared a table of such distribution. The generic terms are 
taken from the index to the Record of Retours ; and as this record relates to pro- 
perties, and not to mere natural objects, the generic terms they contain are to a 
great extent confined to names of places connected with their possession by man, 
and more readily affected by changes in the population. For the purposes of com- 
parison I have framed a list of generic terms contained in Irish topography from 
the index to the Annals of the Four Masters, and of those in Welsh topography 
from a list in the Cambrian Register. I have divided Scotland into thirteen dis- 
tricts, so as to show the local character of the topography of each part of Scot- 
land, and opposite each generic term in Scotch topography is marked, 1st, if it 
occurs in Ireland, and how often ; 2d, if it occurs in Wales ; and 3d, I have 



AND THE DIALECTIC DIFFERENCES INDICATED BY IT. 217 

marked the number of times it occurs in each district of Scotland from the Index 
of Retours. 

On examining this table it will be seen that there are five terms peculiar to 
the districts occupied by the Picts. These are Auchter, Pit, Pitten, For, and Fin. 
Now none of these five terms are to be found in Welsh topography at all, and For 
and Fin are obviously Gaelic forms. 

It is necessary, however, in examining these terms, which may be called 
Pictish, to ascertain their old form. Auchter appears to be the Gaelic Uachter, 
upper ; and as such we have it in Ireland, and in the same form, as in Scotland 
Ochtertire, in Ireland Uachtertire. It does not occur in Wales. 

The old form of Pit and Pitten, as appears from the Book of Deer, is Pette, 
and it seems to mean a portion of land, as it is conjoined with proper names, as 
Pette MacGarnait, Pette Malduib. But it also appears connected with Gaelic 
specific terms, as Pette an Mulenn, the Pette of the Mill, and in a charter of 
the Chartulary of St Andrews, of the church of Migvie, the terra ecclesise is 
said to be vocatus Pettentaggart — "an tagart" being the Gaelic form of the ex- 
pression " of the priest." 

The old forms of For and Fin are Fothuir and Fothen. The old form of 
Forteviot is Fothuir-tabaicht, and of Finhaven is Fothen-evin. 

The first of these words, however, discloses a very remarkable dialectic 
difference. Fothuir becomes For, as Fothuir-tabacht is Forteviot; Fothuir- 
duin is Fordun, but Fothuir likewise passes into Fetter, as Fothuiresach becomes 
Fetteresso ; and these two forms are found side by side, Fordun and Fetteresso 
being adjacent parishes. The form of For extends from the Forth to the Moray 
Firth — that of Fetter from the Esk, which separates Forfar and Kincardine, to the 
Moray Firth. 

An examination of some other generic terms will disclose a perfectly analogous 
process of change. The name for a river is Amhuin. The word is the same as the 
Latin Amnis. The old Gaelic form is Amuin, and the m, by aspiration, becomes 
mh, whence Amhuin, pronounced Avon. In the oldest forms of the language the 
consonants are not aspirated, but we have these two forms, both the old un- 
aspirated form and the more recent aspirated form, in our topography, lying side 
by side in the two parallel rivers which bound Linlithgowshire — the Amond and 
the Avon. There is also the Amond in Perthshire. We know from the Pictish 
Chronicle that the old name was Aman, and the Avon, with its aspirated m, 
is mentioned in the Saxon Chronicle. It is a further proof that Inver is as old 
as Aber in the eastern districts, that we find Aman in its old form conjoined 
with Inver in the Pictish Chronicle in the name Inveraman. 

In Dumbartonshire we find the names Lomond and Leven together. We have 
Loch Lomond and Ben Lomond, with the river Leven flowing out of the loch 
through Strathleven ; but we have the same names in connection in Fifeshire, 



218 MR W. F. SKENE ON THE CELTIC TOPOGRAPHY OF SCOTLAND, 

where we have Loch Leven with the two Lomonds on the side of it, and the river 
Leven flowing from it through Strathleven. This recurrence of the same 
words in connection would be unaccountable were it not an example of the same 
thing. Leven comes from the Gaelic Leamhan, signifying an elm tree, but the 
old form is Leoman, and the m becomes aspirated in a later stage of the language 
and forms Leamhan, pronounced Leven. Here the old form adheres to the 
mountain, while the river adopts the more modern. 

A curious illustration of two different terms lying side by side, which are de- 
rived from the same word undergoing different changes, will be found in Forfar- 
shire, where the term Llan for a church appears, as in Lantrethin. It is a 
phonetic law between Latin and Celtic, that words beginning in the former with 
pi are in the latter //. The word Planum, in Latin signifying any culti- 
vated spot, in contradistinction from a desert spot, and which, according to Du- 
cange, came to signify Cimiterium, becomes in Celtic Llan, the old meaning of 
which was a fertile spot, as well as a church. In the inquisition, in the reign of 
David I., into the possessions of the See of Glasgow, we find the word in its oldest 
form in the name Planmichael, now Carmichael ; and as we find Ballin corrupted 
into Ban, as Ballindoch becomes Bandoch, so Plan becomes corrupted into Pan, 
and we find it in this form likewise, in Forfarshire, in Panmure and Panbride. In 
the Lothians and the Merse this word has become Long, as in Longnewton and 
Longniddrie. 

The Celtic topography of Scotland thus resembles a palimpsest, in which an 
older form is found behind the more modern writing. I shall not detain the 
Society further by going through other examples. The existence of the pheno- 
menon is sufficiently indicated by those I have brought forward, and I shall 
conclude by stating shortly the results of this investigation. 

1st, In order to draw a correct inference from the names of places as to the 
ethnological character of the people who imposed them, it is necessary to obtain 
the old form of the name before it became corrupted, and to analyse it according 
to the philological laws of the language to which it belongs. 

2d, A comparison of the generic terms affords the best test for discriminating 
between the different dialects to which they belong, and for this comparison it is 
necessary to have a correct table of their geographical distribution. 

3d, Difference between the generic terms in different parts of the country 
may arise from their belonging to a different stage of the same language, or from 
a capricious selection of different synonyms by different tribes. 

4th, In order to afford a test for discriminating between dialects, the generic 
terms must contain within them those sounds which are differently affected by 
the phonetic laws of each dialect. 

oth, Applying this test, the generic terms do not show the existence of a 
Kymric language north of the Forth. 



AND THE DIALECTIC DIFFERENCES INDICATED BY IT. 



219 



6th, We find in the topography of the north-east of Scotland traces of an 
older and of a more recent form of Gaelic — the one preferring labials and dentals, 
and the other gutturals ; the one hardening the consonants into tenues — the other 
softening them by aspiration ; the one having Abers and Invers — and the other 
having Invers alone; the one a low Gaelic dialect — the other a high Gaelic dialect ; 
the one I conceive the language of the Picts— the other that of the Scots. 





55 




Scotland. 


Angli. 


Britones. 


Picti. 


Scoti. 


Generic 
Teems. 




m 
H 
■4 




« 3 .5 

a) o <5 




™; <° 

■ — i — 

o-i Q 


is 

s> 

C3 

a 

. 3 

n a 


a 

o 

-a a 

■-3 3 




m 

o 

Em 


O 


«S 

o"Sk" 

° a 
a s 


a Sec 
S3S 


3p= 




Aber, . . 




w 


3 


3 . 


4 






12 


4 


7 


18 


6 






Ard, . . 


66 










. . • 


16 


34 6 


14 


66 


51 


5 


93 


Arn, . . 
















4 


15 


5 












Ar, . . . 




w 






... 


















15 




Auch, . . 


25 












25 




24 


6 


27 


162 


153 


12 


107 


Auchin, 










4 . 


. 23 


88 


34 


30 






22 


8 


25 




Auchter, 










« . • • 


■ ... 


. . . 




6 


10 


6 


12 


4 






Auld, . . 
























33 


9 




... 


Bal, . . . 














36 


63 


90 


88 


127 


67 


59 


56 


39 


Balna, . . 
Bailie, . 


104 










• ••• 


... 








... 




10 




... 


... 


Ballin, . . 






3 


















... 


3 


< > • 






Belloch, 


36 


w 










9 












• * • 








Bellie, . . 


























. , . 


• • • 


... 


14 


Ban, 






















16 












Bar, 










• ■ • • 


'. 27 


66 


6 






• • • 


ri 






90 


19 


Barn, 




• * • 












... 














6 




Blair, . . 










• • • 




16 


51 


29 


8 




ii 


8 






Bo, . . . 












• . • ■ * 






5 








10 






Cam, 


28 








• . • 





11 




13 


8 


8 


54 


15 


4 




Car, . . . 




w 


8 




6 . 


.'. 12 


36 


12 


7 


18 


10 


18 


5 


15 




Col, . . . 














• . • 




7 




• ■ • 


17 








Corrie, . 


















9 








8 




. . . 


Cambus, 
















• • • 


12 














Clon, . . 


93 




.. 






8 


13 








• • • 






7 




Craig, . . 


16 


w 






19 . 


.. 21 


42 


21 


43 


25 


12 


46 


8 


31 


19 


Cors, . . 




w 






... 


.. 14 
















9 




Cul, . . . 


39 












47 




25 


11 


... 


22 


22 


7 




Cumber, 


... 


... 






... 


6 




4 


• • ■ 














Cult, . . 


• • • 
















10 














Dal, . . 


10 


w 


. # 






.. 20 


82 


8 


52 








* • • 


24 




Drum, . 


64 








4 . 


.. 30 


50 


26 


51 


33 


25 


56 


36 


57 


25 


Dun, . . 


95 




3 




6 . 


.. 14 


16 


17 


26 


11 


17 




20 




14 


Fetter, . . 
For, . . 




... 






... 








13 


9 


ii 


4 
22 




... 





VOL. XXIV. PART I. 



3n 



220 



MR W. F. SKENE ON THE CELTIC TOPOGRAPHY OF SCOTLAND. 







< 
« 




Scotland. 




Angli. 


Britones. 


Picti. 


Scoti. 


Generic 
Teems. 


< 


- o 
2 p. 9 


-S5P 

3 a 

§3 


13 3 

L - 

02 Ph 


m 

a 
3 
p 


Be 

a 
a 

<D J 

>1 C3 




.3.5 

-3 a 


3 

Ph 


DQ 

CO 



4.3 


| 




M 
CD 

.a 

< 

Oct! 
a a 

S a 
a 

B-3 


.5 &"& 

^ " t. 
*~ eo — 

a ■ — 
18 3 a 

a S GQ 

S>3 g 


3 
.SP 

-a 
a g 




>* CD 


Fin, . . . 


















14 


6 


4 




3 






Glen, 




35 


W 


5 




17 


42 


44 




56 


. , r 


23 


52 


54 


61 


52 


Gar, 
















34 










17 




23 




Garth, 






W 










10 


23 


13 








... 




10 


Inch, 




90 








... 






18 


30 


25 


10 


17 


31 






Iron, 






• • • 


. . . 










. . ■ 




, . . 








15 




Inver, 




6 






2 


. . * 






5 


32 


10 


16 


37 


69 


■ ■ • 


24 


Kin, 




30 






3 


. . . 






6 


43 


34 


52 


88 


57 




7 


Knock, 




29 




. - . 






5 


64 




6 






32 


30 


37 


31 


Larg, 
Lin, 






w 






... 






... 




5 


8 


... 




13 




Lan, 




3 


w 












. . . 




6 






» • • 




6 


Lath, 




















. . 


9 




. . • 






■ ■ • 


Loch, 




100 


• • • 


• . . 


"7 




14 


34 


16 


30 


18 




15 


19 


26 


, . . 


Locher, 






... 








5 














... 






Led, 
















. . . 


6 


6 














Mon, 




14 










"7 


.. . 




11 


13 


13 


31 


... 






Mul, 




15 


... 


















. . • 




8 






Pen, 






w 


9 


3 




5 


7 


, . , 




• . . 




. . . 


• • • 


2 




Penny, 
Pet, . . 






... 










7 










30 


5 


..." 


11 


Pit, . . 






> ■ • 


• • • 


... 






. . . 




75 


52 


38 


69 


30 


• • • 




Pitten, 














... 






7 


9 








... 




Pol, . 














13 


"7 


6 


9 




... 




17 


9 




Port, . 




22 






• . . 








3 






. . . 






8 




Ra, . . 




63 




• • • 












17 


6 












Strath, . 








• . • 












19 


13 


... 


27 


35 


• . • 


13 


Stron, . 












... 


. . • 


... 






. . . 


. . . 






, . , 


17 


Stuck, - 
















. .. 


8 














6 


Tar, . . 








• > • 


• . . 
















14 






• • • 


Tra, 












. . . 


. • • 










. .. 


. . • 


• . . 


5 




Tom, 


















11 


. • * 




... 








. . . 


Tor, 










11 




11 






. . • 


9 


. . • 


21 


22 


10 


19 


Tullie, . 








... 






. . . 




• . • 




• • • 




38 




... 


. , . 


Tulli, . 








... 




. . . 


. . * 




7 


25 




11 


42 


7 


... 




Tulloch, . 


17 






... 




... 




5 


... 




... 


10 




1 





PLATE XXTI Hqyal Soc ■ > VOL. XXIV 



Eg. 2 




IWMMMMmtmVH 

nmmmtmmtim 



MM.\AMMMAAMMMAl 





m. 4 



JWAMMAWWW 
UMMMMWiWI 



rv, !N from E\& 



vmwmM 

WAAMWWVW 

wttttttmN 








m 5 



2> A 



Kg- 6 




If! A J.KJo>msUn. . EimT. 



( 221 ) 



XVIII. — On the Bands formed by the Superposition of Paragenic Spectra produced 
by the Grooved Surfaces of Glass and Steel* Part I. By Sir David 
Brewster, K.H., E.R.S. Lond. and Edin. (Plate XXII.) 

(Read 7th March 1864.) 

In examining the colours produced by thin laminae of the crystalline lens of 
fishes, I observed a series of rectilineal serrated fringes perpendicular to the 
direction of the fibres, and produced by inclining the laminae in a plane cutting 
these fibres at right angles. I was thus led to imitate these fringes or bands by 
combining grooves or striae cut upon glass or steel surfaces, or grooves taken from 
these surfaces upon isinglass or gums. 

In my first experiments I combined a system of grooves on glass, executed for 
me by Mr Dollond, with a similar system on steel executed by Sir John Barton, 
both of them containing 2000 divisions in an inch. The plate of glass was placed 
above the plate of steel, and slightly inclined to it, as shown in Plate XXII. 
figs. 1 and 2. The glass plate ABCD, fig. 2, was covered with grooves, but the 
steel plate below it was grooved only on the shaded portion abed, the parts AaCc, 
'BbdJ) being polished so as to reflect to the eye at E (fig. 1), the grooves on the 
glass when illuminated by rays, Rr, proceeding from the first pair of the para- 
genic spectra produced by the grooves. 

When the direction of the grooves ac is nearly parallel to the plane of re- 
flexion, and to one another, a series of minute serrated bands is seen on the space 
abed, where the light has been transmitted twice through the grooves on glass, 
and reflected once from those on steel ; but no bands are seen upon AacC, ~BbdD, 
where the steel was only polished. 

When the grooves were slightly inclined to the plane of reflexion, large 
serrated bands appeared upon the spaces AacC, RbdD, and when this inclination 
was increased, these large bands became smaller and more numerous, crowding 
towards Cc and dD. On the other hand, they become larger and larger as the 
direction of the grooves returned into the plane of reflexion. In the azimuth of 
0° they become straight, and by increasing the azimuth, they pass, as it were, to the 
right hand, as shown in fig. 3. 

When the direction of the grooves is inclined to the plane of reflexion, the 
minute serrated bands upon abed become smaller and less serrated. 

* In a very interesting paper on the Spectra produced by Gratings or Grooved Surfaces, M. 
Babinet has given them the appropriate name of Paragenic, in order to distinguish the Spectra 
produced by refraction from those produced by the lateral propagation of light. " Sur la Paragenie 
ou propagation laterale de la lumiere." Paris, 1864. Extrait du Cosmos. 

VOL. XXIV. PART I. 3 O 



222 SIR DAVID BREWSTER ON THE BANDS FORMED BY THE 

When the inclination mriNM. of the grooved plates is increased, the large bands 
become smaller and smaller, and when it is diminished, they become larger and 
larger, getting inclined as in fig. 3, and becoming parallel at 0° of inclination. 

Having been provided, by the kindness of Sir John Barton, with two grooved 
plates of glass containing 500 divisions in an inch, I was enabled to examine the 
fringes on the paragenic spectra under different circumstances. 

When the grooved surfaces of the plates were placed in contact, and the 
grooves formed a small angle with one another, the middle or principal image, A 
(fig. 4), when observed with a lens whose anterior focus coincided with the 
grooves, had no bands, but the paragenic spectra a, c, b, d, on each side had 
numerous serrated bands or fringes perpendicular to the direction of the grooves, 
the number on the first spectra a, b, being at the rate of 1 9 in an inch of the 
luminous disc, and increasing in arithmetical progression. 

When the luminous object is rectangular, and the rectangular paragenic 
spectra are brought nearly into contact, as at ab and cd (fig. 5), the bands, as 
seen at nearly a perpendicular incidence, are shown in this figure. 

When the incident light is inclined to the direction of the grooves, the bands 
suffer no change, and appear immoveable on the surface of the glass plates. 

When the ray of light is perpendicular to the direction of the grooves, and the 
surface of the glass on which they are cut is inclined to the ray of light, the 
bands all descend from a to b (fig. 5), moving off, as it were, at b, and d, and 
succeeded by others when the angle of incidence increases, while they ascend 
from b to a, and from d to c ; moving off at a and c, when the angle of inci- 
dence diminishes. In this case, the grooves of the plate next the eye are turned 
to the left, the opposite motions taking place when they are turned to the 
right.* 

The bands correspond to the intersection of the one set of grooves with the 
other set, and consequently they diminish in number, and recede from one another 
when the inclination of the one set of grooves to the other diminishes, becoming 
parallel to the grooves when the grooves on both plates are parallel. 

Interference bands, parallel to the grooves, may be seen by transmitted light 
upon the paragenic spectra, when two systems of grooves are placed parallel to 
each other, and when the grooves in the one system are parallel to those in the 
other. They are seen both at a perpendicular incidence and when the plates are 
inclined in a plane parallel to the grooves. 

These bands become narrow as the distance of the two grooved surfaces is in- 
creased, and they are seen at all angles of incidence, and in all planes of reflexion 
from the grooved surfaces. 

I have observed those bands, which are generally more or less serrated, in com- 

* This motion of the hands is not seen when the grooved surfaces are perfectly parallel. 



SUPERPOSITION OF PARAGENIC SPECTRA, ETC. 223 

binations of 1000 with 1000, 1000 with 2000, 1000 with 500, 2000 with 500, and 
in the combination of four surfaces of 2000, 1000, 100, and 500. 

In the combination of 1000 and 500, and in no other, a very peculiar system 
of bands is seen with a lens. They are not serrated, and not perpendicular to 
the grooves. The system consists of two sets equally inclined to the direction of 
the grooves, when the grooves in one plate are slightly inclined to those in 
the other. By diminishing the inclination of the grooves, the inclination of the 
bands to the direction of the grooves diminishes, and when the grooves become 
parallel, the bands become parallel and disappear. 

These bands must have a different origin from those previously described, as 
they are similar in number upon all the prismatic images. 

In these experiments the duplication of the bands on the second spectrum, and 
their increase in arithmetical progression on the other spectra, is a remarkable 
fact which it is difficult to explain. The second spectrum differs only from the 
first, and the third from the second, only in their length ; and we can hardly 
suppose that they have a property in a direction perpendicular to their length, 
or to Fraunhofer's lines, which would increase the number of their bands. 

The bands which we have described are more distinct when the spectra are 
pure or formed from a narrow line or bar of light ; but when we wish to see the 
bands on the bar of light or the central image O (fig. 4), the spectra must be 
formed from wide spaces which gave impure spectra. 

In order to examine the interference bands under different conditions, I placed 
(as in fig. 6) a plate of polished steel at different distances from another plate 
of steel, containing six systems of grooves executed by Sir John Barton, varying 
from 312-5 divisions in an inch to 10,000. When the light was reflected twice 
from the grooved surface and once from the plain steel surface, the bands which 
covered the colourless image and the paragenic spectra were splendid beyond 
description, and unlike anything of the kind that I had previously seen. 

1. The bands were parallel to the grooves, or to the lines in the spectra. 

2. They are smaller and more numerous when the grooves are wider or fewer 
in an inch. 

3. They become smaller and more numerous when the distance of the plates 
is increased. 

4. They are smaller and more numerous when the angle of incidence is 
increased. 

5. They become more numerous by increasing the number of reflexions. 

6. They appear like minute black lines upon the colourless image, but when 
their magnitude is increased, they appear like blue or pink bands on a ground of 
a different colour, which is generally white or whitish blue. 

These bands were visible on the systems of grooves, 312-5, 625, 1250, and 
2500 in an inch, but not on the systems of 5000 or 10,000 in an inch. 



224 



SIR DAVID BREWSTER ON THE BANDS FORMED BY THE 



When the spectra had suffered three, four, five, and six reflexions, the central 
and other images were covered with the same number of bands, as with two 
reflexions from the grooved steel; but another series of wider bands was 
superposed. 

The following results were obtained with grooved surfaces having 1250 
divisions in an inch :— 



Distance of plates, 
Distance of circular disc, 
Diameter of disc, 
Angle of incidence, 
Angular diameter of disc, 
Number of fringes on disc, and 
on the first spectrum, 



Oil inch. 
11 55 inches. 

1-317 inch, 
63° 30' 
39° 30' 



Angular breadth of each, 
Distance of plates, 
Angle of incidence, 
Number of fringes on the disc, and "J 
on the first spectrum, . J 

Angular breadth of each, 



7° 50' 

22 inch. 

63° 30' 

10 

3° 55' 



In order to observe the effect produced by varying the angle of incidence, I 
placed a luminous disc three inches and six -tenths in diameter* at the distance 
of nine feet six inches from the grating, and obtained the following results : — 



Angle of Incidence. 

70 

60 



No. of Bands on the Disc. 
29 
21 



Angle of Incidence. 
50 
40 



No. of Bands on the Disc. 

17 
14 



The bands were seen at an incidence of 874°, when the plates were nearly in 
contact. 

The following were the colours seen on the two spectra on one side of the 
colourless image ; but I have not measured the precise angle of incidence at which 
they were seen, nor mentioned in my journal whether they were seen with the 
625 or the 1250 grating : — 





First Spectrum. 




Second Spectrum. 


Great Incidences 


White. 


Great Incidences 


Blue. 




Pale Red. 




Bluish. 




Red. 




Less Blue. 




Purple. 




Bluish White 




Blue. 




White. 




Bluish. 




Pale Red. 




Less Blue. 




Red. 


Lesser Incidences 


White. 


Lesser Incidences 


f Purple. 
i Blue. 



At small angles of incidence, about 42°, the bands become less distinct, and paler 
in colour, the white becoming yellow and the blue brownish. 

In the systems of grooves, whether on glass or on steel, employed in the pre- 
ceding experiments, the part of the original surface not removed by the grooves 
bears a very considerable proportion to the part removed ; but when the grooves 
occupy a large part of the surface, and the intermediate parts a very small one, 
a new set of phenomena are produced, which must change in a remarkable 
manner all the bands of interference. The execution, however, of such systems 



* This disc included part of the spectrum on each side of the bright image. 



SUPERPOSITION OF PARAGENIC SPECTRA, ETC. 225 

of grooves is very difficult. Sir John Barton, with all his experience, failed 
in producing good specimens ; but even with those which he executed for me, 
phenomena of a remarkable kind were exhibited, not only on the .middle or 
colourless image, but upon all the paragenic spectra, varying with the number of 
grooves, but still more remarkably with the angle of incidence* 

P.S. — The preceding experiments were made in 1823 and 1827, and those 
described in p. 223, were repeated in 1838. Having lost or mislaid the glass 
gratings which I then employed, I am not able to compare the bands which they 
produced with a more remarkable series which I have recently obtained with new 
gratings, and which will be the subject of another communication 

* See Phil. Trans. 1829, p. 301. 



VOL. XXIV. PART i. 3 P 



PLATE IXHL JRqyaZ Soo. Trans VOL. 2JW. 



Kg.l 



Kg. 2 



Kg. 3 



K£. 4 




mmww/ftmt 
ammammmmam 
iMMmmmm 

MMAAAAAAAMAAM 
^AAMAAAAMMAAA 



mN^ 




t£ 




Kg. 6 




Kg. 8. 



Rg- 7 



M 




Fig. 10 





Kg. 11 





W.i A.K !,-hi>,-t>m JJm r 



( 227 ) 



XIX. — On the Bands formed by the Superposition of Paragenic Spectra produced 
by the Grooved Surfaces of Glass and Steel. Part II. By Sir David Brewster, 
K.H., F.R.S. Lond. and Edin. (Plate XXIII.) 

(Read 17th April 1865.) 

In the preceding paper I have described the bands produced by gratings or 
grooved surfaces with 500 divisions in an inch, when the two grooved surfaces 
are in contact, and the grooves in the one slightly inclined to those in the other. 

The following results were obtained with two gratings, one of which had 2000 
and the other 1000 divisions in an inch. 

1. When the surfaces are in perfect contact, and the grooves parallel, very 
irregular bands are seen on the united surfaces, either with a lens or by ordinary 
vision, and are parallel to the grooves. They are seen only on the 2d, 4th, 6th, 
&c, spectra on each side of the luminous bar or disc. 

By turning the nearest grating slightly to the right from the azimuth 0°, the 
bands fall back to the left, increasing in number, and descending with their con- 
cave sides downwards into distinct serrated black and white bands, nearly 
perpendicular to the grooves. When the nearest grating is turned to the left, the 
bands descend towards the right, with their concave sides upwards, till they 
become nearly perpendicular to the grooves. In all these positions, the bands are 
twice as numerous on the fourth spectrum as on the second, and thrice as nume- 
rous on the sixth as on the second ; and when the grooved surfaces are perfectly 
parallel, the bands are immoveable on the grooved surfaces at all angles of inci- 
dence. 

2. When the grooved surfaces are separated by the thickness of one or both of 
the plates of glass, the bands are very indistinctly seen, and they seem to dimi- 
nish in size with the distance of the grooved surfaces ; but this is not certain, 
owing to the difficulty of fixing the plates with the grooves at the same inclination 
to each other. 

Similar bands were seen on the united surfaces of gratings of 2000 and 2000, 
1000 and 1000, 500 and 500, 1000 and 500, and 2000 and 500 divisions in an inch, 
but always less distinctly when the grooved surfaces are separated by the 
thickness of one or both of the plates. 

The beauty and distinctness of these bands depend upon the skill with which 
the gratings are ruled. In several of the gratings which I possess, the phenomena 
I have described can hardly be recognised. 

VOL. XXIV. PART I. 3 Q 



228 SIR DAVID BREWSTER ON THE BANDS FORMED BY THE 

When the combined gratings have the same number of divisions, such as 1 000 
and 1000, the bands are seen upon all the spectra, and sometimes very faintly on 
the luminous disc, but when one of the gratings has twice the number of divisions 
as the other, such as 2000 and 1000, the bands appear as already mentioned, 
only on the 2d, 4th, 6th, &c, spectra. In such combinations, the 1st, 3d, 5th, 
7th, &c, spectra of the 1000 grating have no corresponding spectra in the 2000 
grating, with which they can interfere, whereas, when the divisions in both are the 
same, all the spectra of the one are superposed upon all the spectra of the other 
and, therefore, bands are produced upon each of them. 

In like manner, if the number of divisions in the one grating is to those on 
the other as n to 1, n being a whole number, the bands will appear only on the 
spectra n, 2n, 3n, 4w, &c. 

When a grating of 1000 is placed above one of 2000, I have observed faint 
bands upon the spectra, 1, 3, 5, &c, of the 1000 grating, though none of the 
spectra of the 2000 grating could interfere with them. These bands are more 
numerous than those between which they lie, and are doubtless produced by the 
interference of spectra reflected from the plane surfaces of the glass plates with 
those seen by transmitted light. 

When the gratings of 1000 and 2000 are placed at a small angle, as in Plate 
XXIII., fig. 1, the grooves being parallel to AM, and the light incident perpendicu- 
larly, the bands on the left-hand spectra are parallel and rectilineal, and highly 
purple and green, as in fig. 2. 

By turning the gratings round AM as an axis, in the direction from D to B, 
the bands descend from m, as in fig. 3, till they become parallel vertical lines, in- 
creasing in number and less coloured, as in fig. 4, the number of bands on the 
second left-hand spectrum being double those on the first. 

When the rotation is in the opposite direction from B to D, fig. 1, the bands 
rise from n, fig. 5, till they become parallel and vertical as before. 

The opposite effects take place when the gratings are placed as in fig. 6, AM 
and CS being coincident, and when we observe the spectra on the right hand of 
the luminous disc. The bands now descend and ascend from the same points m, 
n, now on the outer side of the spectra. 

When the two edges, AM, CS of the gratings are not parallel, as they are in 
fig. 1, but inclined at a small angle, AMSC, fig. 6, then if, when the fringes are 
parallel at a perpendicular incidence, we turn the gratings round AM as an axis 
from B to D, the fringes descend from m, becoming smaller and smaller, till they 
are parallel and vertical, but when the gratings revolve from D to B, the fringes 
become larger and larger, less numerous, and more coloured, till they are finally 
parallel to AM, the fringes being twice as numerous on the second spectrum as 
on the first. 

When the grooves are perpendicular to AM, as in fig. 7, the bands are faint 



SUPERPOSITION OF PARAGENIC SPECTRA, ETC. 229 

and indistinct. The light being incident perpendicularly, and the gratings turned 
round AM on a plane perpendicular to AM, the fringes do not increase in number 
or greatly change, if the motion is accurately in a plane perpendicular to AM. 

When the gratings are turned in the plane of the horizon passing through 
AM, the side NM approaching the eye, the fringes on the left-hand spectra de- 
scend, increasing rapidly in number, and when the side MN recedes from the eye, 
the fringes ascend, increasing in magnitude and diminishing in number, and are 
highly coloured. At a certain angle, they become parallel to the grooves, when 
by continuing the rotation they move downwards increasing in number and be- 
coming parallel to the grooves. 

In the preceding experiments, the bands are seen on the surface of the gratings, 
but when the grooved surfaces are in contact, and the grooves parallel, bands of 
an entirely different kind are seen, not on the surface of the gratings, but by rays 
diverging from the luminous disc. If we use a long and narrow bar of light, such 
as the opening between the window-shutters, then, when the grooves are parallel 
to the bar, and the grooved surfaces perpendicular to the plane of incidence, the 
bands are parallel to the bar and its spectra. By inclining the grooves to the 
luminous bar, the bands are inclined to the spectra, dividing each of them into a 
great number of spectra, and at an azimuth of 45° the bands become perpen- 
dicular to the spectra. At all these inclinations the bands on the second spec- 
trum are double those on the first, the number increasing in arithmetical progres- 
sion on succeeding spectra. 

When the angle of incidence is increased, the bands increase in number, but 
very slightly with gratings of 1250 divisions in an inch. 

By increasing the distance between the gratings, the bands also increase in 
number. 

Bands similar to those now described are produced with interesting pheno- 
mena by a single grating placed as in fig. 8, so that the image of the grooved 
surface AB, reflected from MN, the lower surface of the glass is superposed as it 
were upon the grooved surface itself. 

1. When the plane of reflexion is perpendicular to the grooved surface, and 
the grooves in the same plane, the bands on the spectra are parallel to the bar 
of light AB, those on the second spectrum being double those on the first. They 
are seen at all angles of incidence, and are larger and more distinct at small angles. 

When the grating is turned round in its own plane, at any angle of incidence, 
so that the grooves form different angles with the bar of light, the bands cross 
the spectra and become perpendicular to them in the azimuth of 45°. The 
paragenic spectra are thus divided into a great number of spectra, the number in- 
creasing as formerly on each succeeding spectrum. 

2. When the grooves are parallel to the bar of light, and the plane of reflexion 
perpendicular to the grooves, the bands are apparently segments of concentric 



230 SIR DAVID BREWSTER ON THE BANDS FOB MED BY THE 

circles at great angles of incidence, the radius of which increases as the angle of 
incidence diminishes, so that they become straight lines at a perpendicular in- 
cidence. The bands are smaller at their upper and lower ends, and those on the 
second spectrum are, as before, double those on the first, as shown in fig. 9. 

In the spectra on the left hand of the bar of light, the concave side of the 
circular bands is towards the bar ; and in the spectra on the right hand of the bar 
of light the convex side of the circular bands is toward the bar. The bands on 
the right-hand spectra are smaller and more numerous than those on the left- 
hand spectra ; and yet, by increasing the angle of incidence, the bands on all the 
spectra increase in size and diminish in number. 

If at any particular incidence we turn the grating in its own plane, the bands 
cross the spectra at angles increasing with the degree of rotation, and becoming 
smaller and more numerous. When the end of the grating nearest the eye (A, fig. 
8) ascends, the fringes, great and small, diminish and become more distinct, and 
the centres of the circles descend. When the grating is turned in the opposite 
direction, the centres of the circles ascend. 

In the principal gratings which I possess, when upon thin glass * including 
those of 1000 and 2000 in an inch, these circular bands are accompanied by 
another system of circular bands, convex to the luminous bar when seen on the 
left-hand spectra, and concave to it when seen on the right-hand spectra ; but, 
what is remarkable, the}' are smaller and more numerous on the first spectrum 
than on the second, as shown in fig. 10. They are best seen when the principal 
circular bands cross the spectra obliquely. 

In the preceding experiments with one grating, the grooves of the reflected 
image are necessarily parallel to those of the real grating, owing to the parallelism 
of the surfaces of the plate of glass, and therefore they cannot exhibit the result 
of superposing two systems of grooves inclined to each other. This condition, how- 
ever, may be obtained by drawing the grooves on the faces of a prism with a small 
angle, or by placing a fluid prism between an ordinary grating and a plate of thin 
parallel glass, which would enable us to vary the inclination of the two sets of 
grooves. A better arrangement, however, is to place the grating AB (fig. 11) 
upon a polished metallic surface, MN. A ray from the luminous bar at R, incident 
on AC at r, reaches the eye at E, after reflexion from the steel surface MN, so that 
the reflected image of the grating, AB, is superposed as it were on the direct image. 

When the grating, AB, of 1000 grooves in an inch is laid upon a steel surface, 
MN, and the grooves are in the plane of incidence, the paragenic spectra of a 
luminous bar are covered with bands, not serrated, parallel to the spectra, exhibit- 
ing all the phenomena already described as seen by reflexion from a single grating. 

* These hands are not seen on a beautiful Munich grating, kindly lent me by Professor Stokes, 
having 3750 divisions in an inch. As the bands become smaller with the thickness of the glass, 
their absence in this grating arises doubtless from its great thickness, which is - 158 of an inch, 
the thickness of the gratings upon which they appear being about 0'04. 



SUPERPOSITION OF PARAGENIC SPECTRA, ETC. 231 

The bands are of the same size as with a single grating when the grooved 
surface is uppermost, but they are very much larger when the grooved surface 
is in contact with the steel. 

When the grooved surface is slightly inclined to the steel surface, as in fig. 
11, and the grooves parallel to the plane of reflexion, a double system of hyper- 
bolic bands is seen, as in fig. 12, having one asymptote coincident with the bar 
of light and the other at right angles to it. One of the systems of hyperbolas 
is on one side of the bar and the other system on the other side, the number of 
bands on the second spectrum being double those on the first. 

When the grooves are inclined to the plane of reflexion by turning them to 
the left or to the right, the double system of hyperbolas moves to the left or to 
the right, the curves of each system crossing the spectra, as in fig. 13, and being, 
as before, twice as numerous on the second as on the first spectrum on both sides 
of the bar. By increasing the inclination of the grooves to the plane of incidence, 
the system of hyperbolas moves farther to the left or to the right. 

When the bar of light is placed at E and the eye at R, fig. 11, the system of 
hyperbolas is inverted, as in fig. 14. 

It is curious to observe the passage of the parallel rectilineal bands into 
hyperbolas, when the inclination of the grooved to the steel surface commences. 
The parallel bands open at their lower end, as in fig. 13, or at their upper 
end, as in fig. 14, and change into hyperbolas. When the light was strong, I 
observed a second but fainter system of hyperbolas lying between the principal 
system and the luminous bar, and caused probably by reflexion from the second 
surface of the grating. The effect produced by the crossing of the bands arising 
from these two systems of hyperbolas was remarkable, and similar to what I had 
observed in combining two gratings of 500 divisions in an inch. This second system 
of hyperbolas was most distinct when the plane of reflexion from the surface of the 
steel was coincident with the plane of reflexion from the glass ; and the double sys- 
tem was seen with grooved surfaces of 500, 1000, and 2000 divisions in an inch. 

In using accidentally a steel surface that was not perfectly flat, I was surprised 
to observe that the bands were not hyperbolas, but circular rings varying in form and 
size with the angle which the grooves formed with the plane of reflexion. In order 
to examine this new and beautiful phenomenon, I placed the grooved surface of the 
grating, AB, upon a convex surface of steel, MN, as in fig. 1 5, so that the rays from 
the luminous body might reach the eye at E, after reflexion from the convex surface, 
MN. The reflected image of the grating is thus superposed upon the direct image, 
and two systems of concentric rings are seen upon the surface of the grating. At 
the point of contact, C, and around it, are seen the rings of thin plates described 
by Newton, and increasing in size with the radius of the surface MN. Around and 
concentric with these as shown at a b, fig. 16, is seen a beautiful system of serrated 
rings formed upon the paragenic spectra, as in fig. 16, the number of rings upon the 

VOL. XXIV. PART I. 3 E 



232 BANDS FORMED BY THE SUPERPOSITION OF PARAGENIC SPECTRA, ETC. 

second spectrum being double those on the first, as before, and becoming narrower 
and closer as they recede from the centre. When the first and second spectra are 
close to one another, as in fig. 17, the rings upon entering the second spectrum 
are doubled, as shown at mmm. These rings are seen only when the grooves 
are inclined to the plane of reflexion. By increasing the inclination, they be- 
come smaller and more distinct, their size being a minimum, and their distinctness 
a maximum, when the azimuth of the grooves is 90°. When the azimuth is 0°, 
or when the grooves are turned into the plane of reflexion, the rings open, as 
at fig. 18, and when turned into azimuth 1° or 2°, those on the side ab, fig. 18, go 
back to the left, and those on the side cd bend into a ring, as shown in fig. 19. 
When the rings are again formed, they increase as the angle of incidence 
diminishes. 

When the rings are increasing or diminishing, or passing from one spectrum 
to another, their centres are sometimes white, and at other times so black as to 
eclipse the rings of Newton. Their colour is very variable, sometimes black, with 
colourless intervals, and sometimes richly coloured with the tints of the spectra 
on which they are seen. When the grating is pressed upon the convex surface, 
or raised slightly from it, the rings exhibit the same phenomena as those of thin 
plates. 

When the ray RR' (fig. 19) from the bar of light, reaches the eye at E, the 
grooves being slightly inclined to the plane of reflexion, the hyperbolic bands 
are seen, as in fig. 12, and when the ray ?V reaches the eye at e, the hyperbolic 
bands are seen as shown in fig. 13, and when the eye receives all the rays be- 
tween R' and r\ the direct and inverted systems of hyperbolas are seen, as in fig. 
20. If, when these are seen, we look at the surface of the grating, we shall see 
the system of concentric rings produced by the union of the two systems of 
hyperbolas. 



( 233 ) 



XX. — On the Influence of the Doubly Refracting Force of Calcareous Spar on 
the Polarisation, the Intensity, and the Colour of the Light which it Reflects. 
By Sir David Brewster, K.H., F.R.S. 

(Read 15th February 1864.) 

It was the opinion of Malus, and adopted by Arago, Biot, and other philoso- 
phers, that the surfaces of regularly crystallised bodies acted upon light in the 
very same manner as the surfaces of ordinary bodies, whether solid or fluid ; or, 
in other words, that the reflecting forces extended beyond the limits of the forces 
that produced double refraction and polarisation. Having been led to question 
this opinion, I undertook an extensive series of experiments on crystalline re- 
flexion, as exhibited in calcareous spar, a crystal peculiarly fitted for this pur- 
pose, from its perfect transparency and great double refraction ; and I published 
the results of these experiments in the Philosophical Transactions for 1819. 

In these experiments, the peculiar action of crystalline surfaces which I had 
expected was placed beyond a doubt. The angle of complete polarisation on the 
surface of the primitive rhomb was found to vary with the inclination of the 
plane of reflexion to the principal section of the crystal ; and with different sur- 
faces the variation of that angle depended on the inclination of the surface to the 
axis of the rhomb. 

As the doubly refracting force thus modified the polarising angle produced by 
superficial reflexion, it became probable that the polarised ray might suffer some 
change from the same cause ; but, after the most careful observation, I could not 
discover the slightest indication of such an effect. Conceiving, however, that 
the change which I expected might be masked by the powerful action of the 
ordinary reflecting force, I thought of reducing it till it was overpowered by the 
doubly refracting force. With this view, I introduced a film of oil of cassia 
between the larger surface of a rectangular prism of plate glass and the surface 
of the spar, and by inclining the prism at a small angle, as in the Lithoscope, I 
was able to separate the image of the sun, or any other light formed by the com- 
mon surface of the prism and the oil, from the image formed by the common 
surface of the spar and the oil, and to examine the properties of the last of these 
images. 

VOL. XXIV. PART II. 3S 



234 SIR DAVID BREWSTER ON THE 

In this way I found that the ordinary reflecting force of the spar was nearly 
reduced to nothing, and was almost entirely under the dominion of the force 
which emanated from the crystal. Light incident on the crystalline surface was 
no longer polarised in the plane of reflexion, but in planes inclined to the prin- 
cipal section of the crystal, the rotation or deviation of the plane increasing with 
the angle which the plane of reflexion formed with the principal section, and was 
so related to the angle which the incident ray formed with the axis of the crystal, 
that the Sine of half the rotation, or deviation, was equal to the square root of the 
Sine of the incident ray to the axis. 

The bearing of these results, as published in the memoir already referred to, 
upon the theory of Light, directed the attention of mathematicians to this subject, 
and I Avas thus induced to resume the inquiry, by investigating the action of sur- 
faces variously inclined to the axis of calcareous spar, — to study the effect of fluids 
of different refractive powers, in reducing the action of the reflecting force, 
and to ascertain the influence of the surfaces thus modified upon light polarised in 
planes differently inclined to the principal section of the crystal. 

Some of the results thus obtained were communicated at different times to 
the British Association, and were found by the late Professor Maccullagh of 
Trinity College, Dublin, to be deducible from the Undulatory Theory ; but other 
results, in which the phenomena were asymetrical with respect to the principal 
section of the crystal were less accordant with theory. Professor Maccullagh was 
therefore desirous to observe the phenomena himself; and having resolved to 
have an apparatus constructed more complex and perfect than the one I used, I 
willingly left the subject in the hands of my distinguished friend. What expe- 
riments he made, or whether he made any, before the sad and sudden close of his 
life in 1847, I have not learned. The subject has therefore again come into my 
hands ; and having been encouraged by Professor Stokes of Cambridge to publish 
my experiments, as having an important bearing on the theory of light, I now 
submit them, incomplete and imperfect as they are, to the consideration of the 
Society. 

The experiments which I published in 1819 were made on the cleavage 
planes of the primitive rhomb of calcareous spar, but those which I am about to 
describe were made on artificial faces, carefully prepared for me by the late 
Mr William Nicol, the ingenious inventor of the polarising prism which bears his 
name. 

I could have wished to repeat some of these experiments with a better appa- 
ratus, and with freshly polished surfaces of calcareous spar, but the sharp vision 
and the sensitive retina of early or middle life are necessary for the observation 
of delicate and almost evanescent phenomena. 

In the following Table I have given the observed polarising angles of the sur- 
faces employed, and of their inclination to the axis of the rhomb :— 



DOUBLY REFRACTING FORCE OF CALCAREOUS SPAR. 



235 



A 

Al 

D 

B 

Bl 

B2 

E 

El 

C 



Inclination to Axis 


0° 




4 


40' 


22 


30 


45 


23 


50 


51 


57 


31 


67 


30 


84 


30 


90 






Observed Polarising 


Angle.* 


54° 


3' 




54 


16 




55 


22 




57 


12 




59 


16 




59 


38 




59 


59 





B. Surface of Rhomb, Inclination to Axis 45° 23'. 

1. With Oil of Cassia, on an Artificial Face. 

Azimuth 90°. Obtuse angle to the right. 

Light polarised 0° and 90°. E' and O'f vanish simultaneously 42|° to the left 
of the plane of incidence, E' being reddish and O' yellowish. 

Light polarised + 45° and — 45°. E' is polarised 45^° to the left. O' vanishes, 
but a little blue light is left, which disappears along with E and O. O' vanished 
more completely by turning the rhomb that gave the images E, 0, 9° or 10° farther, 
from 45° to 55°. 

Azimuth 270°. Obtuse angle to left. 

Light polarised 0° and 90°. E' and 0' vanish simultaneously 33 1° to the right 
of the plane of incidence. A little blue light remains in E' and 0' at the point of 
evanescence. 

Light polarised + 45° — 45° 0' is polarised 35° to the right. E' vanished 
completely. 

2. With Oil of Cassia, on a Natural Face of Cleavage. 

Azimuth 90°. Light polarised 0° and 90°. E' and 0' vanish simultaneously 
471° to the left. 

Light polarised + 45° — 45°. E' is polarised 46° to the left. 0' is scarcely 
visible. 

Azimuth 270°. Light polarised 0° and 90°. E' and 0' vanish simultaneously 
42^° to the right. 

Light polarised + 45° — 45°. 0' is polarised 44^° to the right. E' is nearly 
invisible. 

Common light is polarised 44° to the right. 

N.B. — The evanescence is not complete either on the glass or on the spar sur- 
face ; but more complete on the natural than on the artificial face of the spar. 

Azimuth 38°. Obtuse angle to right. In common sun's light, E' and 0' vanish 
simultaneously at 45° of incidence, and in a plane 82^° to the right of the plane 

* In the plane of the principal section. See Phil. Trans., 1819, p. 158. 

f E' and 0' are the extraordinary and ordinary images from the spar, and E and the same 
' from the prism surface. 



4 



236 SIR DAVID BREWSTER OX THE 

of incidence- The vanishing image is at its minimum when crossed half with blue 
and half with red light. 

Light polarised + 45° — 45°. E' and 0' polarised simultaneously 82 c | to the 
plane of incidence. Both have the same intensity, and are crossed at their 
minimum with red and blue light. 

Light polarised 0° and 90°. Although E does not suffer reflexion from the 
glass surface, yet E' is visible, and vanishes, along with 0', 82^° to the right of the 
plane of incidence. 

Azimuth 218°, Obtuse angle to the Left. Common sun's light is completely 
polarised 8° to the right of the plane of incidence. The evanescence is complete 
at the polarising angle of 0, but not at greater angles. 

Light polarised 0° and 90°. E' and 0' are both polarised 8° to the right. E' 
is bright yellow and 0' bright pink. 

Light polarised + 46° — 45°. E' and 0' are polarised 8° to the right, E' being 
yellow and 0' blue. 

Azimuth 15° to the left. Light polarised Z and 90°. E' and 0' vanish together, 
and 0' is polarised about 40° to the right. 

Light polarised +45° — 45°. Obtuse angle from the eye E' and 0' are 
polarised 55° to the right. 

Azimuth 45°. Light polarised + 45~ — 45°. E' and 0' vanish completely at 
polarising angle 92° to the right. The deviation is increased by increasing the 
incidence. 

On the Intensity of the Reflected Pencil. 

Common Light, Azimuth 0° and 180°. The spar and oil image S is equal to 
about I of the prism image P. 

Azimuth 45° and 215°. S = f P. 

Azimuth 90° and 270 c . S = P, P a little brighter. 

Light polarised + 45°— 45°. 

Azimuth 0° and 180°. 0' gradually diminishes and vanishes at 90°, while E 
increases and is a maximum at 9 G . 

Azimuth 90° and 270°. E' is a maximum and nearly equal to 0', which almost 
vanishes. 

Beyond 90° and 270°, 0' gradually increases while E' diminishes, and they 
become equal at 180°. 

Light polarised 0° and 90°. Azimuth 0° and 180°. 0' almost vanishes, but 
E" is bright, though only equal to £ P. O' increases gradually to azimuth 90°, 
where it is equal to 0. 

Azimuth 90° and 270°. E'= 0', both pretty bright, but less so than P. 

Azimuth 123°. E' vanishes. 0' a little less than P. 

Azimuth 180°. 0' vanishes. E'=|P. 



DOUBLY REFRACTING FORCE OF CALCAREOUS SPAR. 237 



B With Oil of Anise Seeds. 

Azimuth 0° and 180°. E' and 0' vanish together, E' at all angles less than 
45°. and a great part of E, viz. the blue light and more is polarised at angles 
above 45°, a small portion of red light remaining. = E, bluish and ~& yellowish. 

Azimuth 90° and 270°. Change of polarisation 94° to left. Maximum polar- 
ising angle for E' at angles much less than 45°, polarisation nearly complete. 
No appearance of polarisation at great incidences. 0' = E'. 

Azimuth 39° and 321°. Change of polarisation 50° to left. The maximum 
polarising angles commence at the angle of polarisation for O, and the polarisa- 
tion is complete at angles both above and below 45°. 

Azimuth 219°. Change of polarisation 0°, 0' and E' vanishing at the same 
time at about 45°. Above 45°, E' is nearly wholly polarised 15° to the right, 
while below 45°, it is polarised 0°, 5°, 10°, &c to the left as the incidence diminishes. 

With sunlight complete polarisation took place much lower than 45°, and blue 
light was less in this light. 

B. With Oil of Sassafras. 

Azimuth 0° and 180°. No change in the plane of polarisation. 0' is bluish 
and = 4 to 5 E'. 

Azimuth 39°. Change of polarisation about 30°. 

Azimuth 219°. Change of polarisation 0°. 

Azimuth about 60°. Change of polarisation 45°, the polarisation increasing 
at great incidences. 

Azimuth about 70°. Change of polarisation about 50°. Maximum polarisa- 
tion about 48° of incidence. 

Azimuth 90°. No light seems to be polarised at or above 45°. 

Azimuth about 240°. Change of polarisation from 15° at great incidences to 
about 25° at small incidences. Light polarised in plane of reflexion is treated 
nearly as common light, but light polarised 90° out of that plane has a change of 
polarisation a few degrees greater, owing to its being incident at a less angle ; the 
one image from the polarising rhomb being higher than the other. 

B. With Castor Oil. 

Azimuth 0° and 180. O' and E' completely polarised without any change of 
plane. 

Azimuth 39°. Change of polarisation about 10° to left. 
Azimuth 90°. Change about 20° to left at moderate incidences. 
Azimuth 141°. Change 0°. Polarisation complete. 
Azimuth 219°. Change 0°. Polarisation complete. 

VOL. XXIV. PART II. 3 T 



238 



SIR DAVID BREWSTER ON THE 



Azimuth 270°. Change about 1 0° to right at considerable incidences. 
Azimuth 321°. Change 10° to right, and polarisation complete. 



Azimuth 39°. 
Azimuth 90°. 
Azimuth 141°. 
Azimuth 219°. 
Azimuth 270°. 
Azimuth 321°. 



Azimuth 39°. 
Azimuth 90°. 
Azimuth 141°. 
Azimuth 219°. 
Azimuth 270°, 
Azimuth 321°. 



B. Oil of Cajeput. 

Change about 5° to left, and polarisation complete. 
Change 7° to left at moderate incidences. 

Change 0°. Polarisation complete. 

Change 0°. Polarisation complete. 

Change 5° to right at considerable incidences. 

Change 5° to right. Polarisation complete. 

B. With Olive Oil 
Change about 5° to left. 
Change about 100° to left. 

Change 0°. Polarisation complete. 

Change 0°. Polarisation complete. 

Change 8° to right. 

Change 5° to right. Polarisation complete. 



B. With Alcohol highly rectified. 

Azimuth 39°. Change about 1° or 2° to left. The two images vanish at 
different incidences, S at greater than P. 

Azimuth 90°. Change about 1° or 2° to left, spar pencil at angle greater than 
prism pencil. 

Azimuth 141°. Change 0°. 

Azimuth 270°. Change about 1° or 2° to left. 

Azimuth 280°. Change 0°. Polarisation complete. 

Azimuth 321°. Change at 1° or 2° to right. 



A. The Face parallel to the Axis. 

With Oil of Cassia. 
The following observations were made with a plate of glass placed on the 
surface of the spar, the plate being inclined about 5° in the Azimuth 3 parallel 
to the axis. 



Azimuths. 


Change 


of Polarisation. 


0° 




93°* 


10 




85 


20 




80 


221 




74 


30 




55 


40 




59 


45 




55 



Azimuths. 


Change 


of Polarisation 


50° 




47° 


60 




37 


67* 




33 


70 




32 


80 




20 


90 








* The change was 90° at the polarising angle of the spar and oil surface. 



DOUBLY REFRACTING FORCE OF CALCAREOUS SPAR. 239 

These observations were made at angles of incidence considerably greater 
than 45°, the polarising angle. 

The following experiments were made with polarised light. 



Inclination of Plane of 


Inclination of New 


Polarisation to Plane of Incidence. 


Plane to Plane of Incidence 


0° 


0° 


221 


30 


45 


67-L 


67i 


79 


90 


90 



When E' was polarised 90° and O' 0°, O' was nearly thrice as faint as E', and 
much redder. 

When the spar and oil image vanishes, red light is seen on one side, and blue 
on the other side of the vanishing point, as in elliptical polarisation, the rotation 
being different for different colours. 

The following experiments were made with an equilateral prism of glass. 

In Azimuth 0° and 180°. Light polarised + 45° — 45° is polarised + 67°— 67°, 
the change of polarisation being 22°. 

Azimuth about 9°. Light polarised 0° and 90°. E' is polarised 87° to the 
left, and O' and vanish together. Common light is polarised 87° to left. 

Light + 45°— 45°. E' is polarised 59£° to left, and 0' 71 i° to right. E' and 
are equally bright. 

Azimuth about 17°. Light +45°— 45°. E' is polarised 27|° to left, and 0' 
80^° to right. E' is very faint and red. 

Azimuth about 40°. Light + 45°— 45°. Both 0' and E' polarised 25° to left. 
0' is brighter than E', which is faint and bluish. 

Azimuth about 60°. Light + 45 — 45°. O' and E' vanish together a few 
degrees to the left. 

Azimuth 90°. Light +45° — 45°, and light 0° and 90°, are treated exactly as 
by common surfaces ; the prism and spar images undergoing the same changes. 

As the plane of light polarised +°45 — 45°, becomes light +0°— 0°, or is all 
polarised in the plane of reflexion, as the azimuths change from 0° to 90°, the 
inclination of their planes must diminish from 50° to 0°, or from 135° to 0° ; 
that is, from + 67^° — 67^°, to + 0° — °0. 

From the observations with common light, it appears that at angles of inci- 
dence considerably above 45°, it is polarised a few degrees beyond the azimuth of 
90°, and we have no doubt, that at 45°, it is polarised in that azimuth. Hence, it 
follows, that the change of polarisation is equal to the complement of the azimuth, 
or 90 — A. 



240 SIR DAVID BREWSTER ON THE 

A. With Oil of Anise Seeds. 

Azimuth 0° and 180°. Scarcely any effect is produced upon common light at 
any incidence ! The spar pencil is brighter than the prism pencil, and yellow. 

Azimuth between 0° and 90°, and 0° and 270°, the pencil is almost wholly 
polarised at great incidences, and about 90° to the left. 

Azimuth 0° and 180°. Light +45° — 45°. E' was polarised 30|° to left, and 
36° to right. Instead of widening the planes of E' and O' into +67^ — 6'7|, the 
anise seeds oil has brought them nearer into 4- 30^° — 36 a . Conceiving, therefore, 
that an oil of intermediate refractive power might produce little or no change 
upon the light + 45° — 45°, I mixed 2 drops of oil of cassia with 1 drop of oil of 
anise, and obtained the following results. 

A. Oil of Cassia and Oil of Anise Seeds. 
Azimuth 0° and 180°. Light + 45° — 45°. E' is polarised 44° to the left, and 
0° 44° to the right ; that is, almost no change is produced. 

With common light there is not a trace of polarisation, and yet reflexion from 
a transparent surface ! 

Light 0° and 90°. O' vanishes with prism image, and A' polarised about 90°. 

Azimuth 90° and 270°. With common light, the spar and prism image vanish 
together. 

Between Azimuth 0° and 90°. With common light, the polarisation increases 
to about 45° of azimuth, when it is complete, and then gradually returns into 
common light at 90°. 

C. Face 'perpendicular to Axis. 
On the natural surface of the Chaux Carbonate Base. 

Oil of Cassia. 

With common light, the spar image E is polarised 90° out of the plane of 
reflexion, and is then orange, showing that the light polarised 90° is blue. It 
becomes whiter at great incidences, and redder at small ones. The prism image 
O is =2E at 45°. At greater incidences E increases faster than O, and becomes 
nearly equal to it. At small incidences, E decreases much faster than 0, so that 
it follows a different law of reflexion. 

At the greatest incidences which the prism allows, the spar pencil is com- 
pletely polarised. 

Light 'polarised + 45° — 45°. E' is polarised 67° to right, and 0' 67° to left. 

Light polarised 0° and 90°. 0' vanishes with 0, and E is polarised 90° to left. 

Oil of Anise Seeds. 
In all azimuths about -| or-f of E is polarised 90° out of the plane of reflexion ' 



DOUBLY REFRACTING FORCE OF CALCAREOUS SPAR. 241 

at great incidences. At the polarising angle, the light polarised 90° is scarcely 
perceptible. The residual light is reddish, and it is obviously blue light that is 
polarised 90°. 

Light polarised + 45 — 45°, becomes polarised +36 — 36. 



With Alcohol. 

The prism image is completely polarised, and the spar image E equally so 
in the same plane, but at an incidence 3° or 4° greater. 

With oil of sassafras, cassada balsam and water, there is no change in the 
plane of polarisation. 



D. Face inclined 22|° to Axis. 

Azimuth 0° and 180°. In common light, the change of polarisation is 90° to 
the left. It decreases to 20° in azimuth 90°, becomes 0° in azimuth 113°, and in 

Azimuth 180°, it again becomes 90°, decreasing to 0° in azimuth 247°, becoming 
20 in azimuth in 270°, and increasing to 90 in azimuth 360°. 

Azimuth 0° and 180°. Light + 45 —43°. E' is polarised 45* to left and O' 
62f ° to right. 

Azimuth about 15°. Light +45° — 45°. O' is polarised 85^° to left, E vanish- 
ing with O and E the prism images. When O' vanishes E' has reappeared, and 
is red. 

Azimuth 38°. Light +55° — 45°. E is polarised 50° to the right, and O' 
771° to the left. 

Azimuth 20°. E' is polarised 17° to left, and O' 83° to right. 

Azimuth 113. Light +45° — 45'. No change, E' and 0' being both polarised 
in the plane of reflexion. E' nearly vanishes when 0' vanishes ; but by increasing 
the incidence it vanishes completely, showing the usual red and blue at the point 
of evanescence. 

Azimuth 135°. Light +45° -45°. E' is polarised 22° to right, 0'=0 and 
vanishing with 0. 

Azimuth 142°. Light +45°— 45°. E is polarised 31' to the right, 0' vanish- 
ing with 0. 

Azimuth 160°. Light + 45° — 45°. E' is polarised 66° to right, and 0' 22° to 
right. 

Azimuth 218°. Light +45° — 45°. E' is polarised 11° to left, and 0' 77° to 
left. 

Azimuth 90°. Light +45° — 45°. E' and O' are both polarised 28° to the 
left. 

Azimuth 270°. Light +45° = 45°. E' and 0' polarised 18' to right. 

VOL. XXIV. PART II, 3 U 



242 SIR DAVID BREWSTER ON THE 

Azimuth 315°. Light +45°— 45°. E' is polarised 59° to right, and 0' 69° 
to the left. 

Azimuth 322°. Light + 45°— 45°. E' polarised 61° to right, and 0' 83° to right. 

Azimuth 180°. Light +45° — 45°. E' is polarised 5(H° to left, and 0' 58° to 
right. 

Azimuth 0°. Light 0° and 90°. E' is polarised 90° out of the plane of reflexion, 
0' vanishing with 0. 

Azimuth 180°. Light 0° and 90°. E' is polarised to the left, about 86°, 0' 
vanishing with 0. 

Azimuth 270°. Light 0° and 90°. E' and 0' polarised 21° to the right. 

Azimuth less than 270°. Light 0° and 90°. E' and 0' polarised 8° to the right. 

With Oil of Anise Seeds. 

Azimuth 0° and 180°. When the prism pencil with common light vanishes, 
the spar pencil is very bright, and a great deal of light, namely, reddish light 
is polarised in the plane of reflexion. 

Azimuth 90° and 270°. The spar pencil is completely polarised about 7° to 
the left. 

In the azimuth, between 90° and 180° perpendicular to the edge beside the 
obtuse angle, change of polarisation varies from 45° of incidence where it is 0°, 
up to great incidences, where it is about 45° or 50° to the left, the pencil being 
there completely polarised. Between azimuths 270° and 360°, the change varies 
from 125° to 100° at great incidences, but the pencil is nowhere completely 
polarised. 

With Alcohol. 

At Azimuths 0° and 180°, there is no change of polarisation, but the spar 
image is polarised at a much less angle of incidence than the prism image, 
whereas at azimuth 90°, they are polarised at the same incidence. 

E. Face inclined 67° 30' to the Axis. 

In Azimuth 0° and 180°, the change of polarisation is 90°, the polarisation 
being more complete, by considerably increasing the incidence. 

The change of polarisation increases from azimuth 0° to azimuth 90°, diminishes 
from 90° to 270°, and increases from 270° to 369°. 

In Azimuth 0° and 180°. At the polarising angle only half the pencil is 
polarised 90° out of the plane of reflexion, the other half appearing to be polarised 
in another plane. 

Azimuth 0°. Light +45° — 45°. E' is polarised 45° to the right, and 0' 61° 
to the left. 



I 



DOUBLY REFRACTING FORCE OF CALCAREOUS SPAR. 243 

Azimuth 9°. Light + 45° = 45°. E' is polarised 67° to the right, and 0' 55° 
to the left. 

Azimuth about 16°. Light + 45° — 45°. E is poarlised 71° to right, and 51° 
to left. 

Azimuth 45°. Light + 45° — 45°. E' is polarised 90° out of the plane of re- 
flexion, and 0' a few degrees to the left of and E. 

Azimuth about 60°. E' is polarised 76° to left. 0' vanishing with and E. 

Azimuth 90°. Light + 45° - 45°. E' is polarised 70° to left, and 0' 53°. 0' 
is very faint when the prism images vanish. 

Azimuth 180°. Light + 45° — 45°. E' is polarised 68° to the left, and 0' 63° 
to the right. 

Azimuth 0°. Light polarised 0° and 90°. E' is polarised 90° to the left. 0' 
which is reddish, vanishes with 0. 

Azimuth 180°. Light polarised 0° and 90°. E' is polarised 85° to the right. 
0' vanishes with 0. 

With Oil of Anise Seeds. 

Azimuth 0° and 180°. There is no polarisation at great incidences. One-half 
the spar pencil seems polarised 90° to the left, red light being polarised in the 
plane of reflexion. 

Azimuth 90°. Light is almost wholly polarised about 100° to the left at the 
greatest incidences. At less incidences it is half polarised, red light being left. 

With Alcohol. 

In Azimuth 0°, 90°, and 180°, there is no change of polarisation. The spar 
image is polarised at a less angle of incidence than the prism image. 

In order to observe the changes of polarisation in passing from one plane to an- 
other, I had three artificial faces made, slightly inclined to the three principal 
planes C, B, and E. 

E 1. Face inclined 5° \ to C. 

This face was used a few minutes after it was polished. 
Polarising angle in principal section, 59° 38'. 

Polarising angle perpendicular to it 58° 25', much unpolarised light being 
left. 

With Oil of Cassia. 

Azimuth 0°. Light + 45°— 45°. E' is polarised 61° to right, and 0' 73° to left. 
Azimuth 180°. Light + 45° — 45°. E' is polarised 67° to right, and O' 76° to 
■ left. 



244 SIR DAVID BREWSTER ON THE 

In both these azimuths E is ^° with common light, and is yellowish red. 

Azimuth 0°. Light polarised 0° and 90°. E' is polarised 84° to the right. 
0' vanishes with C, and is fainter and redder than E'. 

Azimuth 1 80°. Light polarised 0° and 90°. E' is polarised 90° to right. 
vanishes with 0, and is fainter and redder than E'. 

B 1. Face inclined 5° 28' to B. 

In Azimuth 0°. With bright sun-light the spar pencil E is distinctly polarised 
about 14° to the right. 

Azimuth 0°. Light +45 c — 45°. E' and 0' polarised about 13° to left. 

Azimuth 0°. Light polarised 0° and 90°. E is polarised about 50° to the right, 
and 0' vanishes with 0. 

B 2. Face inclined 12° 8' to B. 

With common light, a small quantity is polarised in the plane of reflexion. 

As the azimuth approaches to 90° on either side of the principal section, the 
light is polarised about 90° out of the plane of reflexion, much bright blue light 
being left. At small incidences the blue becomes brighter and purer. The light 
is orange when the principal section of the analysing rhomb is in the plane of 
reflexion, as if red light was polarised 90' out of the plane of reflexion, and blue 
light in that plane. 

The experiments described in the preceding pages form but a small portion 
of those which I have made, both with artificial and solar light on the action of 
the surfaces of calcareous spar on common and polarised light. In submitting 
them to the Society, it is proper that I should mention the great difficulty of 
obtaining precise results in such observations. The extreme faintness of the re- 
flected light ; its imperfect polarisation in many cases at* the angle of maximum 
polarisation ; and the loss of one-half of the light in the analysing prism, render 
it very difficult to determine the deviation of the reflected pencil, especially 
when it is partially polarised, or unequally double ; and I have been surprised at 
the great difference in the results obtained at different times with the same 
surfaces, when the observations were in both cases recorded as satisfactory. 

The following general results, however, are sufficient to show the importance 
of this class of researches, in reference to certain questions in the undulatory 
theory which have not yet been solved, and perhaps to guide the mathematician 
to their solution. 

1. In the reflexion of light, the surfaces of calcareous spar in contact with 
fluids, act in some cases as ordinary uncrystallised surfaces in the polarisation of 
light. 

2. In reflecting common light, they polarise it out of the plane of reflexion, 



DOUBLY REFRACTING FORCE OF CALCAREOUS SPAR. 245 

the deviation from that plane varying with light of different colours, and with the 
angle of incidence. 

3. In reflecting polarised light, they change its plane of polarisation, some- 
times as in refraction, and sometimes as in reflexion. 

4. In certain azimuths, and at certain incidences when the pencil is not com- 
pletely polarised, much light, apparently unpolarised light, is left ; and in many 
cases, upon all the surface, A, B, C, D and E, the reflected pencil consists of two 
oppositely polarised pencils, as in the reflexion of common light from the surface 
of murexide, chrysammate of potash, and a few other bodies. 

5. The changes in the planes of polarisation, both of common and polarised 
light, are related to the axis of double refraction, that is, to the short diagonal of 
the primitive rhomb of calcareous spar. 



VOL. XXIV. PART II. 3 X 



( 247 ) 



XXI. — Additional Observations on the Polarisation of the Atmosphere, made at 
St Andrews in 1841, 1842, 1843, 1844, and 1845. By Sir David Brewster, 
K.H., D.C.L., F.R.S., &c. 

(Read 2d January 1866.) 

Since the publication of my " Observations on the Polarisation of the Atmo- 
sphere," a long and elaborate Memoir on the same subject, by Dr 11. Rubenson, 
has appeared in the Acts of the Royal Society of Sciences of Upsal.* The obser- 
vations which it contains were made with the finest instruments, and with a 
degree of accuracy which had not been attempted by previous observers. They 
were begun at Upsal in 1859, and carried on at Rome between the 6th of June 
and the 5th of August 1861, at Segni in the Campagna, between the 6th and the 
27th of August 1861, and at Rome from the 5th of October 1861 to the 27th of 
July 1862. 

Although Dr Rubenson has devoted a section of his work to ascertain the cause 
of atmospherical polarisation, another section to the determination of the place of 
maximum polarisation, and a third to the causes which disturb the polarisation 
of the atmosphere, yet the chief object of his labours was to study the daily varia- 
tion of the polarisation of the maximum point ; and so fully has he treated this 
important branch of his subject, that the description of his polarimeter, of his 
method of using it, and the discussion of his observations, with the observations 
themselves, occupy three-fourths of his Memoir. 

In his section on the Cause of Atmospherical Polarisation, Dr Rubenson is led 
to the same conclusion which I had deduced from my earliest observations, 
namely, that the light of the blue sky is polarised by reflexion from the molecules 
of air, and not from vesicles of water with parallel sides, as maintained by 
Clausius, nor, as conjectured by others, from extremely minute drops of water, 
nor from molecules of aqueous vapour in an intermediate state between that of 
gas and that of vesicles. 

According to Arago, the distance of the place of maximum polarisation from 
the sun was 89° 6', the mean of six observations. I found 89° to be the mean of 
a great number of observations, but, like Arago, I considered 90° to be the nearest 
approximation to the place of maximum polarisation. Dr Rubenson found it to 
undergo, as I did, great variations, chiefly from 88° to 92°, the general mean of 

* Series 3d, torn. v. This Memoir has been published as a separate work in 4to, pp. 238. 
Upsal, 1864. 

VOL. XXIV. PART II. 3 Y 



248 SIR DAVID BREWSTER ON THE 

which, from his observations, was 90° 2', half of which is so near to the polarising 
angle of air, which is 45° 0' 32", as to place it beyond a doubt that the light of 
the blue sky is polarised by reflexion from its particles. 

In his section on the Causes which Disturb the Polarisation of the Atmo- 
sphere, Dr Rubenson found, as I did, that clouds and fogs and smoke were the 
cause of the greatest perturbations ; and he also found, as I had done,* that the 
intensity of the polarisation was reduced by the crystals of ice floating in the 
atmosphere which form the halo of 23°. 

Dr Rubenson has not observed the secondary neutral point which I found 
sometimes accompanying the neutral point of Akago, when it rises above the 
horizon, or is setting beneath it, and he has never been able to see, even under 
the fine sky of Italy, the neutral point which I discovered under the sun, and 
which, I believe, has not been seen by any other observer than M. Babinet. 

In 1854, M. Felix Bernard! made several observations at Bordeaux, in order 
to determine the intensity of the maximum polarisation at different hours of the 
day. Though made only on four days of the month of October (from the 16th to 
the 19th inclusive), he found " that in proportion as the sun approaches the 
meridian the value of the maximum polarisation diminishes ; that this value in- 
creases, on the contrary, in a continuous manner as the sun recedes from the 
meridian, and that it reaches its maximum when the sun is very near the 
horizon, the amplitude of this variation being about 009." 

On the 16th October 1854, the maximum polarisation increased gradually after 
mid-day from 25° to 0° of the sun's altitude, from 06236 to 0-7051 ; and on the 
19th October, from 5° to 35° of the sun's altitude, it diminished from 0-7083 to 
06106. On these two days the maximum polarisation, at an altitude of 20°, was 
0-6582, and 0-6464 respectively, the mean of which is 0-6523, differing only 0-12 
from 0*64, as computed from Fresnel's formula by M. Bernard, from my obser- 
vation in 1842, that when the sun's altitude was 20°, the intensity of the maxi- 
mum polarisation at 90° from the sun was equivalent to that which would be 
produced by reflexion from the surface of glass, whose index of refraction was 
1-486, at an angle of 6b° 30' J. 

Before v he became acquainted with the Memoir of M. Bernard, Dr Rtjbenson 
had completed his observations on the same subject ; and, though they lead to a 
similar result, yet they possess a peculiar value from their having been made with 
the finest instruments, in different localities, — in almost all the seasons of the 
3 T ear, and under various states of the atmosphere. 

From a careful examination of his observations, Dr Rubenson arrives at the 

* Treatise on Optics, p. 394, and Edin. Trans., vol. xxiii. p. 226. 
f Comptes Eendus, torn, xxxix. p. 775, October 1854. 

+ Johnston's Physical Atlas — Meteorology, p. 10; or Phil. Mag., series 3d, vol. xxiv. p. 453, 
December 1847- 



POLARISATION OF THE ATMOSPHERE. 249 

general conclusion " that the atmospheric polarisation is subject to a diminution 
during the morning, and to an increase during the evening, without one's being 
able to assign with certainty the precise hour of the minimum polarisation." 
These changes Dr Rubenson found to be often influenced by perturbations com- 
monly of short duration, and taking place indifferently at all hours of the day. 
They frequently arise from clouds or smoke, and probably often from cirrus too 
faint to be seen. According to Dr Rubenson, the blue colour of the sky, in a 
normal state of the atmosphere, and 90° from the sun, is feeble at sunrise, in- 
creases rapidly in intensity, and attains to its maximum some hours before noon, 
the number of hours being different at different seasons. The intensity of the 
colour diminishes towards noon. It then increases, reaches a second maximum 
after some hours, and then diminishes quickly towards sunset. The relation be- 
tween the blue colour of the sky and the intensity of its polarisation, is a pro- 
blem which remains to be solved. 

In 1859, M. Liais made observations on the polarisation of the atmosphere 
during his voyage from France to Brazil, and at San Domingo in the bay of Rio 
Janeiro. His observations were made at the beginning of dawn and at the end 
of twilight, with the view of determining the height of the atmosphere. From 
the observations made at sea he obtained 320, and from the observations made 
on land 340 kilometers, or 212 miles, as the height of the atmosphere* 

The most recent observations on the polarisation of the atmosphere were 
made by M. Andres Poey, between 1862 and 1864, under the tropical sky of the 
Havannah. The observations themselves have not been published ; but he states, 
as one of the most important of their results, that " at sunrise and sunset the 
system of atmospherical polarisation ought necessarily to present two planes of 
rectangular polarisation, one vertical, passing through the eye of the observer 
and the sun, and the other horizontal, with four inversions of the signs, and four 
neutral points 90° from each other." 

M. Poey adopts my theory of atmospherical polarisation, and the analogy 
which I pointed out between the lines of equal polarisation and the isochromatic 
lines of biaxal crystals, and between the same lines and those of uniaxal crystals 
when the sun is in the zenith, — the neutral points now meeting in the sun.f 

It will be seen, from the preceding details, that the subject of atmospherical 
polarisation has become one of the most important branches of optical meteor- 
ology. It has already thrown much light on the constitution of the atmosphere ; 
and when it has been studied in different climates, and at different altitudes 
above the sea, by Alpine travellers and scientific aeronauts, it will doubtless have 
still more valuable applications. 

* Comptes Itendus, &c. torn, xlviii. pp. 109-112 

f See Comptes R-ndus, &c. tom.'lx. p. 781, Avril 17, 1865. 



250 



SIR DAVID BREWSTER ON THE 



Under this impression I have been induced to submit to the Society the rest 
of four years' observations which I made at St Andrews, and which, along with 
those already published, will exhibit the optical condition of the atmosphere on 
many days during every month of the year. 



1841, April 28.— Wind west ; fine day. 

Mean Time. 
3 h p m. Polarisation a maximum in the plane passing through the sun and the 
zenith, and at 88° 16' from the sun. 

When the sun, or the antisolar point, rose or set, 
the neutral line of the polariscope bands, held and 
moved vertically, was a hyperbola, as shown in 



fig. 1. 



■ :vSfr 



1841, April 30. 



Mean Time. 
2 h 5 ro 



Polarisation a maximum in plane of 
zenith and sun, and at 78° 25' from 
sun. 




Horizc 



1841, May 6. 



Fig. 1. 



Mean Time. 
3 h 30 m 



1841, May 8. 



Mean Time. 
10 h 10m 



1841, May 9. 



Mean Time. 

12 h NOON. 



Polarisation, when a maximum, greater in plane of zenith and sun than 
in any other plane. At sunset the difference small. The polarisa- 
tion was greater in the S. horizon than at the same point in the 
N. horizon, probably from the sky being there freer from haze. 



Polarisation, or R, = 25|°, and a maximum in plane of zenith and sun. 
In the N.E., at an altitude of 40°, R = 14£°, and also much less in 
S.W. horizon. 



Sky greenish blue. In plane of zenith and sun R = 13|°. At 4 h R = 
24^° and 22|° in different places, and always greatest where the sky 
was bluest. 



1841, May 11. 



Mean Time. 
3 h 45 m p.m. R = 24^°, and a maximum in plane of zenith and sun. In other planes, 



R = 22J° 



1841, May 12. 



Mean Time. 

10 h 15 m a.m. The sky blue and unusually clear throughout the day. Barom. 301; 
Therm., 9 h p.m. 48°. 
R = 26i° in plane of zenith and sun and a maximum. In other 
planes, 22i c . 
11 40 R = 28J° in plane of zenith and sun. 

21^° in lower planes. 



POLARISATION OF THE ATMOSPHERE. 251 



White clouds ; cumuli in motion. 

Mean Time. 
12 h m R= 27|° in plane of zenith and sun. 
R = 20 ; ?r near horizon. 
R = 25|' at intermediate points. 
1 20 R = 26^ in plane of zenith and sun. 
R = 21|- near E. horizon. 

Near the large white cumuli R diminishes. 

R= 30|° in plane of zenith and sun. 

R = 25l in horizon. 

R = 27^ in plane of zenith and sun. 

11 = 24^ in horizon. 

R = 30|- in plane of zenith and sun. 

R = 28Jr in horizon. 

R=30-| in plane of zenith and sun. 

R = 29i in horizon. 



Jean Time 
4h 30m 


6 





7 


10 


7 


35 


7 


45 



R = 28i in plane of zenith and sun. 
R = 28^- in horizon. 

See Edin. Trans, vol. xxiii. pp. 213-223, for the places of the neutral points on 
this day. 

1841, May 1-1.— The sky in the forenoon has very little blue in it, being in its 
colour a French grey. R less than 14i°. 

Mean Time. 
3 h 30"> R = 141°, and 

R= 18| in a bluer part of the sky. 

According as the thin white haze which masked the blue colour of the sky 
was removed or returned, the place of the neutral points constantly varied in 
their position. 

In the evening the sky became clear, and R became 24^° and 26^°. 

1841, May -16.— See " Edinburgh Transactions," vol. xxiii. p. 223. 

1841, May 16. — Barom. 294. Windy. Considerably above the horizon R 
varied from 17g° to 14^°, as the blue sky was more or less distant from the white 
moving clouds. 

At 7 h , when the blue was purer, R = 22^° at 45° of altitude in the S. 

At 7 h 4^ m R = 241° at 20° altitude in the N. 

1841, May 17.— Barom. 295. 

Mean Time. 
l h 20 m R = 17-o-°, the maximum polarisation at 99° from sun in the plane of zenith 

and sun. 
2 R= 17 J° and 15J C at lower altitudes. 

The following observations, from May 24 to June 3, were made in Edin- 
burgh : — 

1841, May 24. 

Mean Time. 

ll h 10 m R=17i° maximum in plane of zenith and sun. 
R=T1£ in horizon. 
VOL. XXIV. PART II. 3 Z 



252 SIB DAVID BREWSTER ON THE 

After a cloud had passed the polarisation was diminished. 

Mean Time. 
3 h 15 m R=22£° maximum in plane of zenith and sun. 

R=14£ elsewhere. 
5 R=26^ maximum in plane of zenith and sun. 

R=24£ in horizon. 

Babinet's neutral point near the sun. 
7 R = 22J° in zenith and horizon. 

Height. 

7 Arago's neutral point.* 22° 5' 

8 Do. do. 17 48 

9 Do. do. 15 50 



R=:20i 3 in zenith. 
R = 22J in horizon. 



1841, May 25. 



Mean Time. 
6 h m Arago's neutral point in horizon, and the hyperbolic neutral line distinct. 

1841, May 27.— Slightly hazy. 

Mean Time. 
4 h 45"> R = 20i° in zenith. 

R^19^- in horizon. 

Babinet's neutral point not seen. 

1841, May 28. 

Mean Time. 
ll h m R=15^°. Hazy bands, ill-defined and ragged. 

Observations resumed at St Andrews. 
1841. June 3. — In the morning, R = 14^~ and 18^. 

Mean Time. 
6 h m p.m. R=25£° in zenith and horizon. 
6 27 Arago's neutral point not above horizon. 

6 3<> Do. do. very near the horizon. 

6 43 Do. do. above and close to horizon. 

See Edin. Trans, vol. xxiii. p. 214, for the height of Arago's neutral point. 

1841, June 6.— Barom. 29-9. 

Mean Time. 
4 h 45 ra p.m. R=14|° through zenith. 

R=23J 45' above S. horizon. 
R = 22J in S. horizon. 

In and near the horizon, the white bands of the polariscope are bluish on the 
side of the neutral line from the sun. Maximum polarisation more than 90° 
from sun, and diminished by clouds coming on. 

Mean Time. Arago.j 

6 h 0» | r 18° 36' 

8 20 \ Sky verv clear. \ 19 28 

8 30 J ( 21 20 

* The height of Arago s neutral point is to be understood as above the antisolar point, and 
that of Babinet as above the sun. 

t The numbers under Arago and Babinet ai-e the heights of their neutral points above the 
antisolar point and the sun. 



POLARISATION OF THE ATMOSPHERE. 



253 




Sun set. Haze in S.E. 

R = 28J° through zenith, and 26£° 

R=28£ through zenith, and in 

horizon. 
Haze continued. 



in horizon. 

S. and N. 



Arago. 



17° 20' 

21 39 

22 12 



1841, June 8.— Barom. 30. Fine day. 



Mean Time. 
ll h 40 m 



5 
10 
30 
45 

50* 



K = 21i c 
Rr=29j- 
R=26i 
= 28J 



R 



through zenith, 
through zenith, 
through zenith. 



R=19°in W. horizon. 



R = 27° 30' from N.E. horizon. 
45° above N.E. horizon. 
Babinet's neutral point and the neutral hyperbolic line clearly seen. 
R=20° to 24° as the sky was more or less clear. 



At this hour the curious phenomenon shown in the annexed figure was 
seen, two hyperbolic neutral lines meet- 
ing in the sun. 

Mean Time. 



6 h 

7 
8 
9 
9 



42m 

50 

28 

10 

30 



Babinet's N. Point 
above sun. 
13° 24' 



m.+ 



26 
15 
20 
15 



37 

16 

24 









+ 



Fig. 2. 



Mean Time. 
6 h 45™ 



Arago. 



30 
35 
20 
23 
10 
30 



R = 27J° maximum polarisation. 
R=24i° in S.W. horizon. 

Faint clouds near. 



19° 
20 

21 
22 
23 



50' 
25 

10 

6 

41 



1841, June 9— Barom. 209. Fine day ; mackerel-sky occasionally. 

Fine pure sky. R=25£° in N. horizon. 



Mean Time. 
3 h 55"i 




Babinet. 
5° 0' 



R = 26J° + in zenith and horizon. 

Fine cirri above the sun. 
R=28|° in zenith and horizon. 



Antisolar point below horizon. 




At 8 h 40 m clouds suddenly covered the whole horizon. 



* See Edin. Trans, vol. xxiii. p. 221. 

f During the preceding quarter of an hour a stratum of cirri surrounded the neutral point, 



and was just absorbed, when the observation was made. 



254 SIR DAVID BREWSTER ON THE 

1841, June 10. — See " Edinburgh Transactions," vol. xxiii. pp. 214 and 223. 
1841, June 11.— Barom. 29-8. Wind north-east. 

R=26£° in zenith, and 24^° in horizon. 
R = 27° in zenith and horizon. 



Mean Time 


4 h 


45m 


6 


38 


7 


34 


7 


42 


8 


5 


8 


18 


8 


36 


8 


52 


9 


3 


9 


15 


9 


25 


9 


33 


9 


45 


9 


55 


10 






Arago. 


19° 


37' 


19 


3 


19 





18 


52 


18 


50 


18 


32 


19 


12 


19 


17 


19 


20 


21 


37 


23 


39 


25 


22 


25 


13 



Mean of observations within less than 4° of the horizon, 18° 40'. The evening 
was not so fine as yesterday. 

1841, June 12.— Barom. 29-85. Wind north-east. 

Mean Time. 

9 h m a.m. R=24l° in horizon, 26£° in zenith, and 

R=25£ ahout 20° alt. S.W. and S.E. 
11 22 R=24| in zenith. 

1 p.m. R = 23| in zenith. Sky fine. 

The day became cloudy, but suddenly cleared up at 8 h p.m., when R = 28%° 
in zenith and horizon. 



Therm. 50° R= 28£° in horizon. 



21 54 
24 43 

Mean of observations within less than 4° of the horizon, 17° 39'. 

Mean Time. Babinet. 

8 h 25 m 17° 13' 

8 54 17 12 

9 8 17 20 



Mear 


Time 


8 h 


18 m 


8 


36 


8 


52 


9 


3 


9 


15 


9 


25 


9 


33 


9 


45 


10 






2\i a 

17° 


22' 


17 


15 


18 


8 


17 


30 


18 


42 


18 


50 


20 


52 



1841, June 14.— Barom. 296. 



Mean Time. 




7 h 45 m 




7 51 


R=26i° in N.E 


8 5 




8 18 




8 36 





Arago. 
18° 35' 
19 15 
18 53 
18 58 



POLARISATION OF THE ATMOSPHERE. 



255 



1841, June 15.- 


-Barom. 300 at 9 h , and 29-8 at 10 h a.m. 




Mean Time 






Arago. 


8 h 36 m 






18° 45' 


8 52 


R=25i°at 40° alt. N.E. 




18 32 


9 3 






18 9 


9 15 






18 7 


9 40 






21 16 


9 52 


R = 28|° at 40° alt. N.E. 




21 52 


1841, June 21.- 


-Barom. 294. 






Mean Time 






Babinet. 


7 1 * 42 m 


R=24° at 40° alt.. S. 21J° 


in zenith. 


21° 30' 


7 52 \ 






( 20 44 


8 } 


Clouds passing over the neutral point. 


\ 20 


9 15 1 






1 20 28 



1841, June 2.— Barom. 29*68. 

Mean Time 
3 h m p.M. R=14|°. A faint whiteness over blue sky. 

8 31 
R=14|° in horizon, and 25^° in zenith, and 

24£° in alt. 40° S.W. 

9 

9 15 Sky not pure this evening. 

9 30 



8 47 



Arago. 

17° 37' 
] 19 58 

18 45 
18 5 
18 



1841, June 23.— Barom. 2972. Sky impure. 

Mean Time. Arago. 

8 h 5 m ) (21° 30' 

8 23 ( Clouds below the neutral point. Observations J 17 25 

8 45 r not satisfactory. 1 20 35 

8 52 J ( 20 48 



1841, June 27. — After three days of eastern haur and rain. 

Mean Time. 
10 h m a.m. R=19J° in zenith plane, the sky being cloudy. 
1 p.m. R=14i°at20°alt.inE. Barom. 29 6 and rising. 

Arago. 
7 30 21° 21' 

7 45 R=22&° in zenith plane, and 211° at 30 alt. 22 5 



8 

8 18 



21 42 
20 12 



When light clouds covered the sky round and over the neutral point, the 
polarisation was + or vertical from the zenith to the horizon. 



1841, June 28. — After a bad rainy day and the wind east, the sky cleared up 



in the evening and the wind became west. 

Mean Time. 
8 h 50 m p.m. 
9 13 



Arago. 

18° 26' 
18 43 



1841, July 17. — See " Edinburgh Transactions," vol. xxiii. p. 214. 

VOL. XXIV. PART II. 4 A 



256 SIR DAVID BREWSTER ON THE 
1841, July 24. 

Mean Time. Arago. 

6 h 40™ R=14i°; cloudy sky. 25° 55' 

1841, July 28.— Barom. 29'37. A clear blue sky ; cloudy. 

Mean Time. Arago. 

7 h 10 m ") f 18° 12' 

7 40 / R _ 961 o 281C ) 18 43 

7 57 f tt — «>l ^ ^2 < 17 53 



I 



8 10 j ^ 18 5 

1841, July 31. — Cloudy. Neutral point covered with minute cirri. 

Mean Time. Arago. 

8 h m 16° 45' 

8 14 17 25 

1841, August 6. — After two days of rain. 

Mean Time. Arago. 

8 h 5 ra p.m. B=29}°. A cloud had passed. 16° 28' 

1841, August 8. — Morning rainy; splendid evening. 

Mean Time. Arago. 

6^ 50"> R=29|° 16° 17' 

7 5 R=28i 18 20 

7 35 Clouds came on. 17 53 

1841, August 10. — After rain. 

Mean Time. Arago. 

7 h 45^ 18° 15' 

1841, August 17.— Clear and windy. 

Mean Time. 
9 h m a.m. R = 21J° in zenith, and 15|° near horizon. 

The blue of the sky, though very clear, was whitish, which always reduces 
the polarisation. Same day at Perth. 

Mean Time. Arago. 

7 h 15 ra R=24i° in zenith, and 20^° in horizon. 20° 38' 

7 30 19 24 

During the whole day the blue sky became whiter and whiter, and the polari- 
sation fell below 14|° out of the scale of the Polarimeter. Small black clouds 
appeared upon the white sky. 

The observations, from the 6th to the 17th August, were made at the Bridge of 
Earn. 

1841, August 31, September 6th and 12th. See " Edinburgh Transactions," 
vol. xxiii. p. 214. 

1841, September 6. — See " Edinburgh Transactions," vol. xxiii. pp. 215, 223. 
September 12. „ „ „ pp. 215, 223. 



POLARISATION OF THE ATMOSPHERE. 25 ? 



1841, September 13. 



An 


g°- 


19° 


10' 


20 





18 


16 


18 





17 


27 



Mean Time. 
5 h 55 ra A.M. R=25|° zenith; 2 3 |° horizon. 

5 58 

6 32 p.m. R= 251° zenith. 
6 38 
6 42 

1841, September 15.— Barom. 29-61. Splendid day. 

Mean Time. 
10 h m a.m. R = 27 J° in zenith plane, and 25J° in horizon. 
10 18 R=28£°. Maximum 88° from horizon. 

Arago. 
6 p.m. 19° 54' 

6 8 18 18 

6 10 Sky not altogether pure. 18 47 

6 28 R=27|° in zenith plane. 18 5 

1841, September 21.— Barom. 29-95. Sky not pure ; an eastern haur for three 
preceding days. 

Mean Time. Arago. 

4 h 50 m R=15|° in zenith, and 14° 30' ahove S. horizon. 

4 55 Sky whiter in zenith than in horizon. 21° 59' 

1841, September 23. — Barom. 2947. Air damp, but no rain. 

Mean Time. Arago. 

6 h 0™ p.m. R=26£° in zenith, and 17|° 15° alt. S. 13° 30' 

The sky impure. Neutral point covered with small black clouds ; an eastern 
haur supervened. 

1841, September 26.— Barom. 29-25. Day showery. 

Mean Time. Arago. 

5 h 49™ p.m. R=22i° zenith; 26J in horizon. 22° 2' 

6 10 Not free of clouds about neutral point. 20 2 

6 15 The sky purer. 21 50 

1841, September 29. — See " Edinburgh Transactions," vol.xxiii pp. 215, 223. 
1841, September 30.— Barom. 2903. 



MeaE 


Time. 


4 h 


27 m 


4 


37) 


4 


43 


4 


49 



R = 26° in zenith plane, and 25° 10° ahove S. 

horizon. 
Sky whitish. (20° 20' 

Black cloud passed over neutral point. < 19 49 

I 22 29 

1841, October 3.— Barom. 29.8. Wind north-east; cold. 

Mean Time. Arago. 

4 h l m R= 27i° in zenith plane, and 26 J° above horizon. 

4 44 21° 15' 

A cloud passed, and the neutral point descended. 



258 



SIR DAVID BREWSTER ON THE 



1841, October 12. — Barora. 291. Beautiful morning; the sun rose free of 
clouds. 



Mean Time. 
6 h 17 m 
6 24 

4 54 

5 10 



Va.m. R = 28J-° in zenith, and 26|-° in horizon. 
> p.m. R=25° in zenith; 27£° near horizon. 



Arago. 
f 21° 25' 
(18 20 
j 18 1 
(19 57 



1841, October 18 — Barom. 29-5. Wind west ; a very fine day. 



Mean Time. 

3 h m 
4 42 



R=29.y in zenith, and 26. V 3 near horizon. 



Aratco. 



20° 



1841, October 23. — See " Edinburgh Transactions," vol. xxiii. pp. 215 and 224. 

1841, October 25. — A cold day with a little rain. Wind north, and came 
round to the east at 4 h . 



Mean Time. 

3 h 57 m R=29° in zenith plane. 

4 13 I R = 29i-° in zenith plane. 

4 17 V Slight clouds. 

4 23 J R=28f° in zenith plane; 27i° 8° above S. horizon. 

1841, October 2G.— Barom. 296. Fine day and cold. 



R=25J° in zenith, sun shining; 27|° sun not shining. 
Arago's neutral point rose in the N.E. above sea. 
R = 25J° in zenith ; 28J° in horizon. 
R = 29° in zenith ; 29 J° in horizon. 

R=28° in zenith ; 27 A" in horizon. 



'eau 


Time 


2 h 


Qm 


2 


29 


2 


29 


4 


22 


4 


35 


4 


47 


4 


53 


4 


24 


4 


37 


4 


50 


4 


55 



Arago. 
19° 10' 
20 20 
20 31 
20 1 



Arajjo. 



14° 


55' 


22 


17 


20 


40 


20 


35 


22 


39 


Babinet. 


15° 


5' 


15 


55 


16 


55 


15 


36 



1841, October 28.— Barom. 299. Fine day. 

A cloud had just left the neutral point. 
A little cloud left about the neutral point. 



R = 29-i-° in zenith ; 28 £° 10° altitude N. and S. 
Maximum polarisation more than 90° from sun. 
R=26J° in zenith, and at 10° above N. horizon. 



!eai 


l Time 


3 h 


15" 


8 


39 


4 


23 


4 


39 


4 


50 


3 


19 


3 


35 


4 


15 


4 


25 


4 


42 


4 


47 



Arago. 


16° 


48' 


19 


40 


20 


2 


21 


50 


21 


28 


Babinet. 


12° 


15' 


11 


50 


13 


28 


14 


27 


14 


5 



15 



POLARISATION OF THE ATMOSPHERE. 



259 



1841, November 2. —See " Edinburgh Transactions," vol. xxiii. pp. 215 and 224. 
November 4. „ ,, „ 

November 15. — Barom. 295 ; therm. 35. Haze and clouds. 



Apparent Time. 
2 h m 

2 15 

3 56 

4 1 
4 5 

3 41 

3 54 

4 3 

4 7 



R=27i° in zenith and horizon. 



1841, November 16. — R = 30° in zenith; 26i° near horizon. 



Apparent Time. 
3 h 45 m 1 
3 47 / 



Sky whitish blue. 



Ars 


LgO. 


13° 


20' 


18 


10 


17 


40 


19 


50 


Babinet. 


16° 


31' 


17 


55 


16 


36 


16 





Ar 


ago. 


17° 


58' 


17 


10 



1841, November 17.— Barom. 29-43. Frost. See " Edinburgh Transactions," 
vol. xxiii. p. 228. 

Apparent Time. 

ll h 35 m a.m. R=26|° in zenith; 141° near horizon. 
12 Polarisation between the sun and horizon. 



2 


1 


2 


25 


2 


40 


3 


15 


3 


23 


3 


54 


2 


30 


2 


48 


3 


19 


3 


51 



R=29|° in zenith ; 26|° near horizon. 
Fine day and fine sky. 

R=29J° in zenith ; 26A° near horizon. 



Ara 


go- 


14° 


24' 


Babinet. 


11° 


30' 


11 


50 


11 


30 


13 


15 


14 





17 


6 


Arago. 


22° 


31' 


23 


34 


21 


30 


19 






1841, November 23. — Barom. 29-3. Cold, damp day; wind west. 



Apparent Time. 
3 h 57 m 

4 



Arago. 

18° 51' 

Babinet. 

15° 24' 



1841, November 25. — See "Edinburgh Transactions," vol. xxiii. pp. 216, 224. 
1841, Dec. 1. 



Apparent Time. 
4 h 3 m 
4 14 

4 5 

4 10 
VOL. XXIV. PART II. 



R = 28i° ; "30° above S. horizon. 



Arago. 
16° 41' 
17 51 

Babinet. 
15° 34' 
14 52 

4B 



260 SIR DAVID BREWSTER ON THE 

1841, December 5. 

Apparent Time. 

ll h m a.m. R=25|° in zenith plane. 

1841, December 7. — Neutral line convex towards the sun. 

Apparent Time. Babinet. 

8 h 51 ra a.m. 15° 4' 

1841, December 11. — Barom. 294; therm. 41. 

Apparent Time. Arago. 

3 h 46 m R=28l in zenith, and in 20° above horizon. 18° 27' 

3 51 16 16 

Although the sky appeared free of clouds, yet, upon close examination, ex- 
tremely faint and transparent clouds reflecting no light, but rather darker than 
the sky, covered the whole heavens. 

1841, December 17. — Beautiful morning. 

Apparent Time. Babinet. 

9 h 7 m a m. R = 27|° in S.W. horizon. 

9 13 Neutral line concave to sun. 13° 10' 

10 30 R=27|-° in zenith plane; 25|°, 30° above N.E. horizon. 

1841, December 18. — Splendid sky; without a cloud. 

Apparent Time. Babinet. 

8 h 53"» a.m. 15° 55' 

Arago. 
9 8 19° 52' 

At 9 h the maximum polarisation R=28° in zenith plane, and far beyond 90° 
from the sun. 

Apparent Time. Arago. 

3 h 17 m pm. 19° 5' 

3 32 17 25 

Babinet. 
3 22 R=28° in zenith ; 27i° in horizon. 17° 20' 

3 36 18 25 

1841, December 22. — Fine frosty day ; clear sky. 

Apparent Time. Babinet. 

9 h 23 m 14° 10' 

Aiago. 
9 33 20° 10' 

R = 27|° in zenith plane ; 24-|-° in S.W. horizon, and 26£°, 10° above. 

1842, January 6. — Fine day. 

Apparent Time. Arago. 

2 h 34 m 19° 6' 

Babinet. 

2 38 16° 18' 

R=2i° in zenith plane ; 28^°, 30° above E. horizon. 






POLARISATION OF THE ATMOSPHERE. 261 



1842, January 7. — Very fine day, with haze. 



Apparent Time. 
9 h 18 m A.M. 

12 



11 52 

12 4 p.m. 

12 9 R = 22|° in zenith. 



Babinet. 


15° 


51' 


13 


53 


Arago. 


20° 


34' 


22 





22 


37 


20 


40 


19 


49 



3 25 

4 17 

At 9 h 18 m . R = 24 , a maximum in horizon. The neutral line was convex to 
the sun. Sky clear, without clouds. 

1842, January 16. — Ground everywhere covered with snow. 

Apparent Time. Babinet. 

4 h 12 m 19° 25' 

1842, January 17. — Fine clear day ; therm. 36. 

Apparent Time. Babinet. 

8 h 37 m a.m. R = 24|° at 35° alt. 201° in horizon. 16° 55' 

3 47 p.m. R= 25° in zenith; 24 J° in horizon. Neutral 
line concave towards the sun. 

1842, January 21. — Barom. 29.77 ; dry, frosty day. 

Apparent Time. Arago. 

•jh c>4.m JR=27|° maximum polarisation in zenith) 1f . 4f) , 

\ plane, and 24|° near horizon. J 

Babinet. 

3 31 19° 3' 

1842, January 25. — Snow covers the ground. Barom. 294. 

Arago. 
Arago' s neutral point in horizon. 
R= 17i° in zenith plane, and + 15° in horizon. 

16° 45' 
R=:18|° in zenith, and 15° in horizon. 19 21 

R=18|° in zenith, and at 50° altitude, 15°.16 20 

Babinet. 

17° 20' 

18 30 

1842, January 27.— Barom. 29-2 ; therm. 36° at 8 b 30 m . 

Apparent Time. Arago. 

oh oA-m ( R=24A° near horizon ; neutral line concave 

8 n 34 m a.m J. • , 2 ' 

( to sun. 

2 20 p.m. 11° 50' 

4 37 20 40 
2 32 R=25° in zenith plane and S. horizon. 
. nr f Thin clouds, almost invisible everywhere but \ , o° n ±A> 

\ above the sun J 



Apparent Time. 


l h 


12 m P.M 


2 


15 


2 


12 


3 


40 


2 


15 


3 


36 



262 SIR DAVID BREWSTER ON THE 

1842, January 28. — Barom. 29 6. Fine day; fresh. 

Arago. 
13° 5' 

>2 i 21 15 

20 25 
19 41 
Babinet. 
18° 48' 
18 10 
16 52 

1842, January 29.— See " Edinburgh Transactions," vol. xxiii. pp. 216, 224. 
1842, February 2.— Very fine day, and clear sky till 2 h . 

Apparent Time. 
ll h 30 m a m. Arago's neutral point not risen. 

R=25° in zenith plane, 20J° in horizon. 

Arago. 
2 p.m. A thick, impure sky. 16° 50' 



Apparent Time. 

2 h 7 m p.m. 


R = 22J° in zenith ; 


25^° in E. horizon. 


3 23 




R=26J° in zenith; 


27£° in S.E.. and 


1 


in S.W. horizon. 




3 43 








4 5 








3 21 








3 47 








4 2 









1842, February 3.— Fine day. 



Apparent Time. Arago. 

4 h 43 m 20° 20' 

Babinet. 
4 45 22° 1' 

1842, February 4. — Barom. 3015. Fine day; cloudy. 

Apparent Time. Arago. 

3 h 14^ R=20i° in zenith, 24|°, 50° alt. W. horizon. 18° 40' 

n j R = 25° in zenith, thin whitish clouds, 24^° in "1 „„ „_ 

\ E. horizon, 10° alt., 22£ 3 in alt, 20 c W.horizon.j U 6 ' 

4 44 20 14 

1842, February 5. — Barom. 30-05. Fine day ; sky perfectly clear. 



Appar 


ent Time. 


l h 


51 m 


1 


44 


3 


48 


4 


9 


4 


31 


3 


51 


4 


7 


4 


33 


9 


5 A.M. 


12 


34 p.m. 



R = 28i° in zenith, 26-|-° to 18£° on E. horizon, 
neutral line convex to sun. 



R = 27^° in zenith. 

R = 22£° 30° alt. S.W. horizon. 

R = 27i° in zenith, 20 J° in horizon. Dark haze 

in horizon from E. to W. hy N. 
R = 272° in zenith to 14£° in horizon. 



An 


igo. 


17° 


25' 


23 


10 


22 


15 


20 


50 


20 


30 


Babinet. 


17° 


20' 


19 


42 


20 


38 



1842, February 10. — Fine day, but cloudy. 



Apparent Time. 


Arago. 


2 h 57 m 


R=24i°, 25° above W. horizon. 16° 45' 


3 58 


19 20 


4 45 


R = 26|-° in north. 17 43 




Babinet. 


3 59 


R = 29° in zenith, and at alt. 30° E. horizon. 18° 38' 


4 5 


19 4 


4 41 


21 50 



Clouds came on, followed by great rain and wind, at 10 h p.m. 



POLARISATION OF THE ATMOSPHERE. 



263 



1842, February 11.— Rain in the forenoon till 2 h 30 E 

Apparent Time. 
3 h lfl m 

3 55 R = 29|- in zenith. Sky quite clear. 

R = 29| in zenith. Sky quite clear. 



R = 24i° 30° above S.E. horizon. 



4 20 
4 38 

3 22 

3 53 

4 23 
4 36 



R = 28i° in zenith, and in N. horizon. 



R = 29J-° in zenith. Neutral line convex to 
sun." R = 28-i-° 15° alt. 



Arago. 


17° 


33' 


21 


8 


19 


45 


20 

Bab 


5 

inet. 


16° 


19' 


17 





19 


34 



18 36 



1842, February 12. — Barom. 29"3. Rainy, with wind. Cleared up at 4 h . 



Apparent Time. 
4 h 18 ra 

4 20 
3 55 



Arago. 



Clouds passed away. 



R = 24J°, but reduced to 20 J° when watery 
clouds passed over the sky from W. to S. 



r 17° 28' 

< Babinet. 
I 17° 12' 



1842, February 15.— Rain in morning, then fine day. Wind west.* 

R= 27|° in zenith to 221° in S.E. horizon. 



Apparent Time. 

4 44 
4 55 



Babinet. 
21° 58' 
20 24 
Barom. 3005, therm. 43° ; wind west. 20 30 





Seco 



Clouds came into S. horizon at 4 h 55 m , and the whole of the N. and N.E. horizon, 
especially above the sea, was covered 6° or 8° high with a dark band of distant 
haze. 

N.B. — At 3 h 48 m , when the neutral point was 
1° 57' high, there was just above the sea horizon, H H, 

a portion mn of + bands, a continuation of those m — v^tp|$j1fc[^ — " 
on the sea, so that there were two neutral points 
here. These were more fully developed at 3 b 58 m , as Hj 
shown in a former paper.f 

1842, February 16.— Barom. 30-164 

At noon, sun's alt. 21°, there is clearly a faint 
neutral point a little above the horizon, and 19° below 
the sun. 

At 2 h 48 m , though the bands at Arago's neutral 
point are all +, as in fig. 4, they are most weak- 
ened at m n, which is the effect of the secondary 
cause. R = 19^° in zenith, and in both horizons at 
25^ alt. 

Fig. 4. 

* See Edin. Trans., vol. xxiii. pp. 216, 224. 

f Ibid., vol. xxiii. p. 222. + Ibid., vol. xxiii. pp. 217, 228. 

VOL. XXIV. PART II. 4 C 



Fig. 3, 




264 



SIR DAVID BREWSTER ON THE 



At 3 b 10 m the weak polarisation at m n now extends down to H H. R = 22£ 
in zenith, and in horizon at 25° alt. 

_l_ At 3 h 44 m the two neutral points are developed, as in 

the annexed figure, the — hands x x being just dial 
■ I i.f.j tinctly visible. 

1842, February 18.— See "Edinburgh Transactions," 



x : 



H- 



-H 



vol. xxiii. pp. 217, 229. 

1842, February 19. — Fine day, with wind. 

Arago. 



Fig. 5. 
Apparent Time. 

2 h 58 m R = 26i° in S.E. horizon, alt. 20°. 

3 7 Neutral point 2° alt. 13 Q 38' 

3 20 Secondary neutral point seen. 14 42 

4 15 Fleecy clouds over neut. point. R = 24±° S. hor. 20 
4 40 R=24i° in zenith plane. 19 28 

1842, February 21.— From 4 h 52 m to 4 h 57 m , a secondary neutral point to that 
of Arago was gradually but imperfectly developed.* 

1842, February 22. — Dull, cold morning, which cleared up about l h 25 m , when 
R = 21i° in clear sky, from which clouds had passed. 



Apparent Time. 



Arago. 



3 h 24 m R = 25f° in zenith, 22£° near W. and E. horizon. 15° 40' 
3 38 17 29 

( Negative bands do not touch the sea horizon. | .. 

\ Secondary neutral point in the horizon. j 



4 2 

4 28 

5 8 

4 6 

4 24 

5 6 



Pol. of moon, R = 3°; R = 27£° in zenith. 



20 50 
23 8 
19 2 

Babinet. 

17° 15' 
16 19 
19 5 



1842, February 24.— Barom. 290. 

Apparent Time. Arago. 

3 h 47 m 17° 20' 

2 32 R=26|° in zenith, 27£° in S.E. horizon. 

3 51 R = 23| in zenith, and 25|° at 35° alt. N.W. horizon. 

1842, February 25. — Dull day ; frost in morning ; cleared up at 4 b 2 m . 



Apparent Time. 



Babinet. 



5 h 9 m R = 28° in zenith, 26£° in E. and W. horizon 17° 50' 



5 12 



Arago. 
18° 5' 



* See Edin. Trans., vol. xxiii. pp. 217, 224, 228. 



POLARISATION OF THE ATMOSPHERE. 265 

1842, March 2. — A wet day, the place of the sun being seen as a white spot. 

Apparent Time. 

2 h 20 m The polarisation everywhere extremely feeble. Babinet's neutral point was 
nearly 75° above the horizon, or about 54° above the sea ! See March 16. 

1842, March 4.— Cloudy and sunshine. 

Apparent Time. 

l h 18 m R = 25i° in zenith, and 22J C at 30° alt. W. horizon. 
1 48 One plate of glass at 60° incidence compensates the polarisa- 
tion on the sea horizon opposite the sun. 
3 h 53 m Arago. 

3 58 11° 13' 
5 23 12 22 
5 26 17 55 

Babinet. 
5 38 R=27|° in zenith, and 22|-° in horizon. 17° 22' 

1842, March 7.— ll h 30 m R = 28J° in zenith, to 18^° in horizon, but at l h 30 m , 
after showers of hail and rain, R = 22i° in zenith. 

1842. March 10. — Sky clear, and wind in west. 

Apparent Time 

ll h 0" R = 27J° in zenith. 

Neutral point seen below sun. 

R = 28° in zenith, 24 J° in horizon. 

Arago's neutral point not risen. 

The + bands scarcely seen in horizon. 

R = 28° in zenith. 

Arago. 
12° 55' 
13 56 

. „_ f The secondary neutral point just touching the sea 1 . . _ 
1 horizon. J 

1842. March 13.— 12 h 36 m R = 26£° in zenith. Sky clear. 

Apparent Time. Arago. 

4h 27m The breach in the + bands not completed. 12° 15' 

4 39 But at 4 h 39™ the neutral point is formed. 12 6 

Both on the 10th and 13th Arago's neutral point is above the horizon, though 
masked by the cause which produces the secondary neutral point. Over a space of 
3£° above the sea horizon, the + bands almost wholly disappear before the — ones 
are perceptible, and the neutral point is distinct on the sea horizon. 

1842, March 16. — Barom. 29-96, the sun occasionally shining through a 
thickish haze in a sky without blue. Wind slight in south-west. 

Apparent Time. 

10 h 45 m Polarisation the same as on March 2 ; Babinet's neutral point 
30° above the sun, or more than 60° above the horizon ! 

1842, March 17.— Barom. 29-77. Much rain last night. Wind west; white 
clouds flying. 

Apparent Time. 

10 h 20m R = 26i° in zenith plane, and soon after 24£°. 
10 50 R=20|- in zenith plane, and in a clear sky, over which 
clouds have passed. 



11 


15 


3 


14 


4 





4 


10 


4 


13 


4 


15 


4 


20 



266 



SIR DAVID BREWSTER ON THE 



1842, March 18. — Barom. 2909. Wind and rain, day cold, and wind in west. 



Apparent Time. 

3 h 27 m R = 25°, diminishing to 20°. 
5 28 



R=30° in zenith plane. 



5 


55 


6 


12 


5 


30 


5 


57 


6 


10 



Arago. 
15° 48' 
18 10 
17 48 

Babinet. 
19 : 10' 
17 40 
20 12 



1842, March 19.— Barom. 290. 

Apparent Time. 

3 h 54 m Polarisation of moon, 20i°; R = 23° in zenith. 
4 39 R= 24° in zenith plane; sky very clear. 

Polarisation of moon, 20|°; R = 22J°in zenith. 
R = 2fjJ° in zenith plane. 

1842, March 24.— Cleared up at l h . Fine day. 



5 


44 


6 


14 


6 


19 


5 


48 


6 


12 


6 


21 



Arago. 
10° 37' 
19 45 
18 47 

18 45 

Babinet. 

19° 30' 

19 45 
17 26 



Apparent Time 
2 h 
4 R = 20|° in zenith plane. 



m R=22i° 50° above the horizon. 



1842, March 26. — Barom. 29-3. Cold wind from point north of west. 



Apparent Time. 
5 h 49 m 



16 
31 



5 52 R= 281° in zenith plane. 

6 34 



Arago. 
18° 32' 
19 25 

18 4 
Babinet. 
19° 20' 

19 40 



1842, March 28.— Sky clear. 

Apparent Time. 

4 h 20 m R = 26^° in zenith plane, and 18 c and 20° in horizon. 

1842, March 29 h . 

Apparent Time. 
6 h 20 ra 
6 36 

6 18 

1842, March 30.— Wind ; flying clouds. 

Apparent Time. 

6 h 27 m R = 28i°in zenith, to 23£° in horizon. 
6 45 
6 52 
6 24 



48 
10 



R=r21|° in zenith plane. 



Arago. 
17° 55' 
17 50 


Babinet. 
18° 40' 


Arago. 
18° 13' 
17 55 
19 37 


Babinet. 
20° 40' 
19 54 



POLARISATION OF THE ATMOSPHERE. 267 

1842, April 2. 

Apparent Time. Arago. 

6 h 5 m 19° 15' 

7 4 19 42 

Babinet. 
6 36 18° 5' 

6 38 19 8 

7 4 20 18 

1842, April 3. — Fine clear sky ; hail in the afternoon. 

Apparent Time. 

1 1>, ACrr, f Brewster's neutral point most distinctly seen. 1 1o0 •. 

ll n 4o m I tv . * > lo 

I Distance trom sun, J 

1842, April 5, 6, 8.— See "Edinburgh Transactions," vol. xxiii. pp. 217, 225, 
and 229. 

1842, April 9.— Barom. 30-16. Wind east; bitterly cold. 

Apparent Time. Arago. 

3 h 25 m R= 221° in zenith plane. The sky clear. 

5 46 22° 7' 

6 651 M , ,, f 15 20 

7 o) Effectoff °g- I 1 6 2 

Babinet. 

5 49 R=15i° in horizon. 17° 10' 

6 57 19 30 

Between 5 h 49 m and 6 h 57 m a fog came on, and there were no neutral points. 
1842, April 10. 

Apparent Time. 

4 h 5 m R=18J° in zenith, and 14£° in horizon. 

4 22 R=27 in zenith, and 14J in horizon. 

Babinet's neutral point very near the sun, and no neutral point seen below 
the sun. 

1842, April 13.— Barom. 30-12. Fine day* 

Apparent Time Arago. 

5 h 48 m 16° 20' 

6 20 17 55 

6 54 19 40 

7 10 19 45 
7 19 R=30£° in zenith. 19 4 
7 29 R=32|° in zenith. 22 10 

R increased from 25° at 4 h to 32£° at 7 h 29 m . 

1842, April 15. — See " Edinburgh Transactions," vol. xxiii. p. 230. Haze 
from west. 

Apparent Time. 
5 h 40 

5 48 

5 57 R= 14£°, in zenith 18i°, 20° ahove N. horizon. 

6 28 White nebulosity. 

7 

5 50 

* See Edin. Trans., vol. xxiii. p. 225. 
VOL. XXIV. PART II. 4 D 



Arago. 


16° 


25' 


18 


40 


18 


21 


18 


50 


Babinet. 


28° 


20' 



268 



SIR DAVID BREWSTER ON THE 



1842, April 16. 



Apparent Time 


5 h 


54 m 


6 


31 


6 


59 


7 


21 


7 


35 


7 


46 


5 


58 


6 


33 


6 


57 


7 


23 


7 


37 



Arago. 

17° 25' 

22 22 
R = 27|° in zenith, 22£° in N. and 18|° in S. horizon. 19 50 

18 55 

45 

23 50 



R=18|° at moon. 



R = 23J° in zenith, much less in horizon. 
R=23° in zenith, 21° in W. and 181° in E. horizon. 19 

20 
R=29J°in zenith, and 24 J° in both horizons. 17 

R=z31° in zenith, and 29|° in horizon. 17 



Babinet. 

25° 40' 

8 

3 

45 

35 



1842, April 17.— Slight haze. 

Apparent Time. 

„ h „ 0m f Brewster's neutral point distinctly seen, R=19£° in 



5 34 

6 3 

7 35 



\ zenith, and 12° in S. horizon. 



Babinet's neutral point just risen. 
R = 28£ in zenith plane. 



Arago. 



R=17J° in zenith, 22^-° in horizon; clear sky. 20° 10' 



Babinet. 
19° 30' 



1842, April 18.— Barom. 30-0. 

Apparent Time. 

7 h 14m Pol. moon = 27|°, 29£° in zenith. 



7 23 



Pol. moon=:28£ , 30J° in zenith. 



Babinet. 
18° 45' 

Arago. 
17° 45' 



1842, April 19. 

Apparent Time. 



7 20 
7 37 



Pol. moon 14|° and a maximum. 

22^°, and maximum 26£°. 



Arago 
16° 35' 

Babinet. 
18° 15' 
19 10 



1842, April 20.— See " Edinburgh Transactions," vol. xxiii. pp. 218, 230. 



1842, April 21.— 

Apparent Time. 
ll h 30™ R=23|-°, maximum at 90° from sun. 

1 10 R=25£°, maximum at 90° from sun. 



7 20 
7 48 

7 22 



A fog came on. 



p. 222. 



Arago. 

17° 55' 
14 24 

Babinet. 
20 15 



POLARISATION OF THE ATMOSPHERE. 269 

1842, April 22.— Fine day. 

Apparent Time. 
ll h 10 m A.M. R=17|°; maximum polarisation in zenith 90° from sun. 

Brewster. 

2 R= 27° at 90° from sun in zenith plane. 12° 10' 

3 R=29 at 88 from sun in zenith plane. 11 10 

4 10 R= 29 £° at 90° from sun. 

Arago. 
6 55 20° 25' 

Babinet. 
6 58 Thin clouds. 22° 15' 



1842, April 24.— Barom. 2984, rising. 

Apparent Time. 

{A haze. Babinet's neutral point 70° high ; Brewster's 
not yet risen. After the haze had increased the sky 
cleared. 
6 21 Altitude of Arago' s neutral point above horizon. 8° 40' 

6 10 „ „ „ 13 

6 10 Secondary neutral point exactly in horizon. 

1842, April 25, 26, 27, 28, 29.— See " Edinburgh Transactions, 1 ' vol. xxiii. pp. 
218, 230. 

1842, May 2.— Barom. 29-93 ; wind east. 

Apparent Time. Arago. 

6 h 18 m 23° 45' 

7 1 R=22|° zenith to 18|° in horizon. 24 45 
7 45 20 15 

Babinet. 
6 21 Ii= 28 1° maximum in zenith plane. 16° 30' 

1842, May 3* — China-ink sky; wind east. 

Apparent Time. 

9 h m a.m. R = 19|° maximum polarisation in zenith to 14 J° in horizon. 
11 R= 19£° maximum polarisation in zenith to 14 J° in horizon ; 

bands ragged. 

Arago. 

11 29 R=20°; maximum at 89° from sun. 10° 15' 

12 15 R = 20°. 9 25 



1842, May 4. 



Apparent Time. Arago. 

5 h 56 m 

fi _ f The — bands of secondary neutral point distinct, 1 ,_ <>,, 

\ and this point commenced. J 

6 13 '20 46 

6 16 The secondary neutral point distinctly formed. 21 1 



* See Edin. Trans., vol. xxiii. p. 230. 



270 SIR DAVID BREWSTER ON THE 

1842, May 9.— Barom. 29-83. 

R = 22|° in zenith plane. 

Bands all positive. 

Positive bands still in horizon. 



pan 


>nt Time 


5h 


42m 


6 


7 


6 


18 


6 


39 


7 


28 


6 


45 


7 


30 



Arago. 


19° 


15' 


22 


47' 


23 


21 


Babinet. 


15° 


0' 


16 


5 



R=19£° in zenith plane. 

1842, May 15, 16, 17.— See "Edinburgh Transactions," vol. xxiii. pp. 218,230, 
231. 

1842, July 16.— At Lacock Abbey, Wiltshire. 

R=23° in a singularly fine day, this low polarisation indi- 
cating nebulosity, which collected and produced rain. 

1842, August 2.— At St Andrews; Barom. 300. 

Apparent Time. 

5 h 9 m R=20£° in zenith, and I4£° in horizon. 

_ „,_ f The bands opposite the sun begin to weaken, and 

\ there is a second neutral point. 
6 15 Negative bands distinctly seen. Arago. 

6 20° 36' 

6 26 25 1 ! 

7 29 23 1 
7 54 22 41 
9 13 33 40! 

Babinet. 
6 32 13° 40' 

( Arago's secondary neutral point distinctly formed. A dark 
\ band along the horizon, below Arago's neutral point. 



6 39 



1842, August 4. — Slight rain in morning ; Barom. 29-5 ; wind west. 

Apparent Time. 

5 h 54 m R=25|° near horizon. 

6 41 Arago's secondary neutral point in horizon. 

7 6 R = 29i-° in clear 'blue sky. 
7 9 Altitude of Arago's neutral point above horizon, 15° 40 

1842, August 5. — Rain in forenoon. I observed a singular sky in the west, 

to the north of the sun and below him. The whole sky, 
from A A to the horizon H H, was clear, but the part 
A A was darker than B B, and of a deep China-ink 
blue, while B B was much paler. But, what was sin- 
gular, these differently coloured spaces were separated 
by an irregular line m m m, showing that the whole 
Flg ' 6 ' space m mm H H was a thin sheet of cloud or 

vapour, terminating abruptly at mmm. 

Apparent Time. 

5 h 40 m R=17|°, maximum polarisation at alt. 40°. Arago. 

7 21 R=27|° in zenith plane, and 26|° at alt. 40°. 17° 10' 

7 25 A cloud approaching the neutral point. 16 35 

7 40 R=28J°, maximum in zenith plane. 19 30 



A 


Darker Blue. 


A 


m 

B 


m 

Pale Blue. 


m 

B 


H 


Whitish. 


H 



6 


W] 


6 


46 


7 


40 


8 


4 


7 


43 


8 


10 



POLARISATION OF THE ATMOSPHERE. 271 

1842, August 6.— Barom. 29*6; rain at 5 h p.m. 

Apparent Time. 

7 h 50 m R=28|° max. in zenith plane to 24|-° in horizon. 

7 56 Altitude above horizon of Arago's neutral point. 19° 10' 

Clouds around the blue space. 

1842, August 11.— Barom. 2962; rain in morning. 

Apparent Time. 

5 h 30 m R = 23|° in zenith plane, and 20^° in S. horizon. 

5 51 + Bands opposite sun almost gone at 1|° above hor. 

Arago. 

6° 40' 

14 35 

20 35 

Altitude of the two neutral points above the horizon.^ 22 20 

Babinet. 

18° 25' 
R= 29° in zenith. [ 12 

1842, August 17.— See "Edinburgh Transactions," vol. xxiii. p. 231. 
1842, August 22.— Warm ; fine day. 

Apparent Time. 

oh oom / R=24|° maximum polarisation in zenith plane to 

\ 19|° in horizon. Arago. 

5 52 18° 36 

6 37 R= 27 J° in zenith plane. 21 16 

7 26 R = 28i in zenith plane. 19 56 
7 49 22 8 

Babinet. 
7 52 13° 8' 

1842, August 28. — See "Edinburgh Transactions," vol. xxiii. p. 231. 

1842, September 9. — Barom. 291, after rain. 

Apparent Time. 

5 h 53 m R = 26J C maximum polarisation in zenith, to 25 J° in horizon. 

Arago. 
6 38 18° 57' 

1842, September 13.— Barom. 2993. Fine day. 

Apparent Time. 

4 h 39 m R = 28° maximum polarisation in zenith plane. 



Arago. 
4 50 ( horizon, to 24^° in horizon. In S. horizon, alt. |> 15° 35' 



R = 27-2° maximum polarisation in 30° alt. N.W. 
horizon, to 24^° in horizon. 
30° 261° to 22 \° in horizon. 



18 35 
R = 29i-° maximum polarisation. Pol. of moon 19J°. 20 17 

20 
16 24 
Babinet. 

R=29° maximum polarisation in zenith. 14° 25' 

15 40 

R = 29^° maximum polarisation in zenith. 16 6 

19 8 
VOL. XXIV. PART II. 4 E 



5 


29 


5 


58 


6 


36 


7 


2 


5 


31 


5 


56 


6 


38 


7 


6 



272 SIR DAVID BREWSTER ON THE 

1842, September 17. — Barom. 29 - 45, after a rainy day. 



Apparent Time. 
6 h 48 m p m. 

6 53 



R = 28|° maximum polarisation in zenith. 



Arago. 

17° 20' 

Babinet. 
16° 25' 



1842, September 18 — Fine blue sky. Barom. 29*57. 



Apparent Time. 

3 h m R=21|° in zenith plane to 19£° in horizon. 

R=22£ in zenith plane to 20|- in horizon. 
R=25° in zenith plane to 23° in horizon. 
Fringes all + opposite sun and in horizon. 



3 45 

4 20 
4 46 

4 47 

5 6 
5 36 
5 56 
5 21 



R = 27|° max. polarisation in zenith to 24J 3 in hor. 



1842, September 28.— Fine day. 

Apparent Time. 

4 h 32 m R = 28° maximum polarisation in zenith plane. 

4 58 

1842, September 29.— Fine day ; cold ; wind east. 

Apparent Time. 

4 h 37 m R=30^° maximum polarisation in zenith. 

5 11 

1842, September 30.— Fine day. 



Arago. 
15° 28' 
16 36 
20 16 
19 40 



Arago. 

18° 36' 

Arago. 
17° 34' 



Apparent Time. 
4 h 18 m 
4 24 

4 55 

5 47 

4 58 

5 44 



R=29*° max. polarisation in zenith to 26^ c in hor. 
Neutral point not risen. Bands + . 



R=:29 1 f maximum polarisation in zenith plane. 



1842, October 15— Fine day. Barom. 30'0, rising. 

Apparent Time. 

4 h 32 m R = 29|° maximum polarisation in zen. to 26|° in hor. 



5 


11 


5 


42 


4 


34 


5 


9 


5 


46 



Arago. 


16° 


11' 


18 


18 


Babinet. 


15° 


23' 


17 


28 


Arago. 


18° 


0' 


18 


11 


25 


30! 


Babinet. 


15° 


23' 


17 


26 


20 






1842, October 19.— Barom. 29 3. Cold. 

Apparent Time. 



4 h 56 m 
5 5 



R = 27-2° maximum polarisation in zenith plane. 



19° 11' 
20 9 

Babinet. 
16° 39' 






POLARISATION OF THE ATMOSPHERE. 273 

1842, October 20.— Barom. 29-62. Fine day; cold. 

Apparent Time. Arago. 

4 h 15 m R=26i° near S. horizon. Clouds in zenith. 14° 46' 

1842, October 21. 

Apparent Time. Arago. 

4 h 49 m Neutral point above a cloud. 18° 13' 

1842, October 24.— Barom. 29*33. Rain in the morning; cold. 

Apparent Time. Arago. 

4 h 28™ 18° 46' 

Babinet. 
4 32 R = 27° maximum polarisation in zenith plane. 21° 59' 

1842, November 9.— Barom. 29 -06, after a storm of wind and rain. 

Apparent Time. Arago. 

4 h 41 ra Polarisation of moon in S. horizon 25J°. 17° 20' 

1842, November 14.— See " Edinburgh Transactions," vol. xxiii. pp. 218, 226. 
1842, November 15.— Barom. 2972. Hard frost in morning. 

Apparent Time. Arago. 

2 h 12 m Secondary neutral point in horizon. 17° 50' 

1842, November 20, 21.— See " Edinburgh Transactions," vol. xxiii. pp. 219, 226. 
1842, November 27. — Barom. 29*15, rising. A dark band along the horizon. 

Apparent Time. 

3 h 57 m R=27° in zenith, and 18|° in horizon. 

Arago's secondary neutral point in horizon, and primary one consider- 
ably up. 

1842, December 3.— Barom. 29*95. Fine day. 

Apparent Time. 
12 h 46 m Arago's neutral point not risen. 

12 46 R=27J° maximum polarisation in zenith, 20|° in hor. 

Arago. 

2 16 R=28|° maximum polarisation in zenith, 18|-° in hor. 19° 20' 
4 23 24 22 

Babinet. 
4 28 20° 15' 

1842, December 17. — Barom. 29-58, rising after rain. 

Apparent Time. Arago. " 

3 h 16™ 18° 5' 

Babinet. 

3 19 R = 29° maximum polarisation in zenith. 17° 50' 

1842, December 18. — Barom. 29-79. Raining occasionally. 

Apparent Time. Arago. 

ll h 13 m 13° 45' 

12 23 14 42 



274 



SIR DAVID BREWSTER ON THE 



1842, December 22.— Barom. 29-38, falling. Rain. 



Apparent Time. 
2 h 43 m 

2 46 



R = 29° maximum polarisation in zenith plane. 



1842, December 23.— Barom. 29-01, after rain. 



Apparent Time. 
3 h m 



R=30° maximum polarisation in zenith plane. 



1842, December 24.— Barom. 2933. 

Apparent Time. 
12 h 3 m R = 26^° maximum polarisation in zenith plane. 

E = 28 0- 
R=27 
R=29 
R=27i° 
R = 29i 



12 


44 


1 


32 


2 


24 


3 


8 


3 


37 


2 


27 


3 


5 


3 


39 



f The point of maximum polarisation rising as the "1 
\ sun's altitude diminishes. J 



1842, December 26. — Barom. 2888. 

Apparent Time. 

l h 3 m R=26i° maximum polarisation, alt. 30°. 

3 27 



3 30 



R = 28° maximum polarisation in zenith plane. 



Arago. 

17° 50' 


Babinet. 
16° 10' 


Arago. 
18° 16' 


Babinet. 
19° 4' 


Arago. 

15° 28' 


15 


5 


17 


30 


18 


40 


17 


52 


19 


14 


Babinet. 


18° 


28' 


20 


6 


17 


55! 


Arago. 
16° 25' 


17 


15 


Babinet. 
17° 40' 



1842, December 27— Barom. 29*35. Sun shining through a dry haze : which 
continued all day. The lines in the sun's spectrum singularly sharp. 



Apparent Time. 
Hh 48 m 

12 4 

1 45 

2 35 

3 15 

12 9 

1 50 

2 38 



Arago. 
R=26J° maximum polarisation in zenith plane. 15° 50' 

{R=23^ maximum polarisation in zenith plane, "1 .._ . 
141° in horizon. j 17 15 

R=24° maximum polarisation in zenith plane. 20 25 

R=27J° „ „ 21 30 

19 
Babinet. 
12° 25' 
14 40 
16 5 



R=29| 



1842. December 28.— See " Edinburgh Transactions," vol. xxiii. pp. 219, 226. 
1842, December 29.— Barom. 2950. Clear in north. 



Apparent Time. 
11^40™ 
12 



11 44 



R=26|° maximum polarisation in zenith plane. 1 

Slight clouds. 



R=28J° alt. 50°. Sky clearer. 



J 



Arago. 
15° 25' 
15 29 

Babinet. 

17° 49' 



POLARISATION OF THE ATMOSPHERE. 275 

1842, December 30.— Boisterous day; thin white clouds. 

Apparent Time. Arago. 

2 h m R = 22|-° maximum polarisation in zenith plane. 

2 24 15° 5' 

1842, December 31.— Windy, and sky cloudy. 

Apparent Time. Arago. 

ll h 53 m R=27-2° maximum polarisation in zen. Sky impure. 16° 40' 

1843, January 4.— Fine day. 

Apparent Time. Arago. 

ll h 32 m R = 27|° maximum polarisation in zenith. 14° 41' 

11 43 14 30 

Babinet. 

11 35 R = 23i° to 18°. Haze coming on. 15° 47' 

1 51 Altitude of Arago's neutral point above hor. 4° 30'. 

R = 24J° to 18-|-°. Haze to east and south. 

1843, January 5. — At Rankeilour M'Gill ; clear and cold. 

Apparent Time. • Arago. 

iih 97m / R = 28 J° maximum polarisation, 18|° in horizon. "1 ., . .,, 
\ Neutral line convex to sun. J 

1843, January 10. — Barom. 28*5 ; very cold. 

Apparent Time. Arago. 

2 h 3 m R = 29° maximum polarisation in zenith plane. 14° 25' 

2 41 Polarisation of moon 21 J°, 24^° in horizon. 

1843, January 11.— Barom. 28-72. Fine day. 

Apparent Time. Arago. 

1 9 h ^rn / R = 26J-° maximum polarisation. Nebulosity in 1 -. _ , r, 
\ zenith. J 

1 47 R = 29|° maximum polarisation in zenith. Clear sky. 

2 55 R = 28° maximum polarisation. Slight nebulosity. 19 50 

3 10 Polarisation of moon 15°. 

1843, January 21. — A misty day. 

Apparent Time. Arago. 

2 h 46^ R=19J-°maximumpolarisationin zenith 30° at 14°alt. 16° 40' 

3 18 Misty. 10 6 

The mist increased, and the maximum polarisation everywhere reduced to 
14|°, and the two neutral points descended to the horizon several degrees. 

1843, January 28.— Barom. 29-45. Very windy. 

Apparent Time. Arago. 

12 h 28 m Neutral point below horizon. 14° 10' 

12 47 „ „ 14 
1 57 „ „ 11 5 
3 51 Misty. 22 41 ! 

Babinet. 
3 54 R = 28J,° maximum polarisation to 20^° in horizon. 

12 28 R = 26|- „ „ to 18| „ 14° 45' 

VOL. XXIV. PART II. 4 F 



276 



SIR DAVID BREWSTER ON THE 



1843, January 30 — Barom. 29-50. Windy. 



Apparent Time. 

12 h 18 m 



1 47 

2 28 



3 55 

3 



{ 



Arago. 

Neut. point below horizon, R = 21°, maximum clear. 15° 40' 
Neut. point below horizon, R = 24J° in zenith to \-in 9 c 



14|° in horizon. 



} 



11 29 



_ 2 ( R=28J° maximum polarisation in zenith, to 21 J° "> 1 „ ~ q 
\ in horizon. J 



18 32 

Bahinet. 
19° 0' 



._ J R=27|° maximum polarisation in zenith, to 21£° ),„ ot- 
\ in horizon. j 



1843, February 15. — Very cold day; clear only in north. 

Apparent Time. 
2 h 57 m 



Arago. 
16° 5' 



1843, February 16. — Barom. 29-18, rising. Fine sky. 

Apparent Time. 
ll h 56 m R=25° maximum polarisation, 20° in horizon. 

12 57 



12 57 



3 28 



( R=29-J° maximum polarisation in zenith, 24 }/ 
\ in horizon. 

( R=29£° maximum polarisation in zenith, 26|-° 
(^ in horizon. 

R=30° 



Babinet. 

9° 40' 
Brewster. 
11° 25' 

Arago. 
1 12° 52' 

| 18 40 

17 52 
14 52 
17 26 



1843, February 17. — Barom. 29*6. Sky not clear in N. horizon. 



Apparent Time. 
3 h 6 m 
3 30 



Arago. 
11° 28' 
14 14 



1843, March 4.— Barom. 30-08. 



Apparent Time. 
3 h 35m 

3 46 

3 54 

4 6 



R=14|-° maximum polarisation in zenith plane. 



Arago. 
16° 45' 
17 30 

Secondary neut. point 50' high. Hazy in horizon. 17 57 

20 30 



1843, March 7. 

Apparent Time. 



4 b 40 m R=24J° maximum polarisation in zenith. 



Arago. 
17° 0' 



1843, March 8.— Barom. 30-13. Wind east ; hazy. 

Apparent Time. 

4 h 14 m ll=24|° maximum polai'isation. 



Arago. 

17° 47' 



POLARISATION OF THE ATMOSPHERE. 277 

1843, March 12. — Barom. 2934, after rain. 

Apparent Time. Arago. 

4.h om / R = 25|° maximum polarisation. Polarisation I .„ c , „ 
\ of moon 7°. J 

1843, March 25.— See " Edinburgh Transactions," vol. xxiii pp. 220, 226. 
1843, March 28— Barom. 29-84. Wind east ; dry. 

Apparent Time. Arago. 

6 h 2 m 16° 45' 

1843, March 29.— Barom. 29-88. Fine day, cold ; wind east; dry. 

Apparent Time. Arago. 

3 h 51™ R=28|°, 25J° in S. and 26|° in W. horizon. 

5 58 18° 35' 

6 26 19 33 

Babinet. 
6 1 R=29|° maximum polarisation in zenith, 28° in hor. 18° 22' 

6 24 R=29|° „ „ „ 18 27 

1843, April 7. 

Apparent Time. Arago. 

6 h 54 m 19° 0' 

Babinet. 
6 48 16° 29' 

1843, April 10.— Barom. 2974. Very cold wind, north-west. 

Apparent Time. Arago. 

6 h 23« 20° 42' 

Babinet. 
6 25 22° 23' 

1843, April 11.— Barom. 2980. Very cold. 

Apparent Time. Arago. 

6 h 43 m R = 28J° maximum polarisation. Sky whitish blue. 17° 30' 

6 48 17 45 

1843, April 12.— Barom. 2977. 

Apparent Time. Babinet. 

4 h 35 m 41° 35'! 

The sky was covered with a thick haze ; the sun barely seen through it, and 
showers of hail falling occasionally. The bands a maximum above the sun, 
but disappeared 9° above horizon. A neutral point was seen at 25° alt. opposite 
the sun, but the bands below it seemed 4- ! though extremely faint. 

1843, April 17.— See " Edinburgh Transactions," vol. xxiii. p. 226. 

Apparent Time. Arago. 

6 h 30 m R=25 *° maximum polarisation in zenith, 201° in hor. 22° 32' 

7 4 R=29 „ „ " „ 20 44 
7 30 R = 29| „ „ „ 20 10 



278 SIR DAVID BREWSTER ON THE 

1843, April 19.— Nebulosity in zenith. Clouds round horizon. 

Apparent Time. Arago. 

7 h 30 R = 25|° maximum polarisation in zenith plane. 18° 35' 

Babinet. 
7 33 19° 0' 

1843, April 28.— Barom. 29*44, after rain. Clear sky after clouds had cleared 
away. 

Apparent Time. Arago. 

7 h 9 m 20° 23' 

7 40 19 37 

Babinet. 
7 3 R = 29° maximum polarisation in zenith plane. 16° 46' 

7 44 R = 29 maximum polarisation in zenith, 20 -J ° in hor. 18 

1843, April 29.— See "Edinburgh Transactions," vol. xxiii. pp. 22G-27. 
1843, April 30.— Barom. 30-07. Morning, and rising. Not a cloud. 

Apparent Time. 

l h m R = 26V maximum polarisation in zenith, 22£° in horizon. 

4 15 R = 26| 

5 43 Secondary neutral point forming. 

Arago. 

6 4 11° 20 

6 52 Rz=29°. maximum polarisation in zenith, 22^° in hor. 19 20 

7 33 R = 29| maximum polarisation in zenith, 22;V in hor. 19 35 
7 58 19 3 

A brown haze rising up upon the blue sky. See " Edinburgh Transactions," 
vol. xxiii. p. 231. 

1843, May 2.— Barom. 3007. Wind east; no sun. 

Babinet's neutral point near zenith, and polarised bands scarcely seen, except- 
ing at 90° from sun. 

1843, May 3.— See " Edinburgh Transactions," vol. xxiii. p. 227. 

Apparent Time. Arago. 

6 h 49 m 18° 26' 

Babinet. 
6 53 R=30° maximum polarisation in zenith, 27° in hor. 14° 20' 

Very clear in zenith, with a whitish sky. 

1843, May 6.— Wind east ; uniform China-ink clouds over the sky, through 
which the sun shone brightly, but ill-defined. 

4 h 4 3 m .— Polarised bands distinct over the face of the sun and above him, but 
exceedingly feeble opposite the sun. 

1843, May 11.— Barom. 30 0. Fine day. 

Apparent Time. Arago. 

2 h 30 m R = 20J° maximum polarisation in zenith plane. 

6 Neutral point not up. 14° 34' 

6 12 R=23|-° maximum polarisation in zenith. 18 15 

Whitish- blue sky. White clouds in horizon. 



POLARISATION OF THE ATMOSPHERE. 279 

1843, June 13.— Barom. 30. Wind east 

Apparent Time. Arago. 

6 h 56 m 19° 15' 

9 10 20 25 

Babinet. 

7 R = 27jj° maximum polarisation in zenith plane. 25° 10' 

9 13 R=29| in zenith, horizon clear. 15 30 

1843, June 14. — Barom. 30-07. Splendid day ; wind east. 

Apparent Time. Babinet. 

Qh 12m R = 29±° maximum polarisation in zenith, 21|° in hor. 13° 30' 

7 59 R = 29J° „ „ 22J in hor. 15 30 

Arago. 

fR = 29J° maximum polarisation in zenith, 22|° in 1 1]0 
\ horizon. Neutral point in horizon. J 

7 56 18 20 



1843, June 15.— See "Edinburgh Transactions," vol. xxiii. p. 231. 
1843, June 16.— Barom. 30*0. Sky covered with white nebulosity. 

Apparent Time. 

12 h 20 m R = 25J° maximum polarisation in zenith plane. Arago. 

7 10° 45' 

7 38 17 50 

Babinet. 
7 41 R = 29|-° maximum polarisation in zenith plane. 15° 55' 

1843, June 21.— See " Edinburgh Transactions," vol. xxiii. pp. 220, 227, 
1843, June 22.— Barom. 29-90. Wind east ; fine day. 

Apparent Time. Arago. 

8 h 42 m Antisolar point in horizon. Clouds in zenith. 19° 15' 

1843, June 23.— Barom. 2992. Fine day. 

Apparent Time. Arago. 

7 h 17 m R=25° maximum polarisation in zenith, 18|° in hor. 15° 35 

7 26 17 30 

8 58 18 30 

Babinet. 

7 30 15 10 

9 R = 27|-° maximum polarisation in zenith, 22° in hor. 16° 50' 

1843, June 24.— Barom. 29 92. 

Apparent Time. Arago. 

7 h 8 m 17 C 47 

1843, June 26. 

Apparent Time. Arago. 

7 h 25m 21° 6' 

8 52 Neutral point in the middle of a bright orange cloud. 17 33 
VOL. XXIV. PART II. 4 G 



14 


15 


17 


32 


19 


30 


18 


15 


Babinet. 


13 


40 


16 


3 


17 


11 



280 SIR DAVID BREWSTER ON THE 

1843, July 3.— Barom. 29-57, rising. 

Apparent Time. Arago. 

7 h 29 m R = 26° maximum polarisation in zenith, 20£° in S. hor. 16° 28' 

1843, July 6. 

Apparent Time. Arago. 

6 h 50 m R—.28J maximum polarisation in zenith, 22i° in hor. 11° 45' 
7 1 

7 21 R= 181° polarisation of moon. 

8 13 R = 29° maximum polarisation in zenith plane. 
8 55 

7 25 

8 15 R=28£ c polarisation of moon. 
8 52 

1843, July 11.— Barom. 30-0, rising. 

Apparent Time. Arago. 

6 h 55 m R=29J° maximum polarisation in zenith ; clear sky. 12° 28' 
7 51 White clouds forming in many places. 21 11 ! 

Babinet. 
7 54 19° 10' 

1843, July 21.— Barom. 295 ; no rain. 

Apparent Time. Arao-o. 

7 h 34 m Thin clouds in zenith and near sun. 20° 4' 

1843, July 24.— Barom. 2987, rising; no rain. 

Apparent Time. Arago. 

6 h 58"> 17° 52' 

1843, August 6.— Barom. 2977, after a wet day. 

Apparent Time. Arago. 

7 h 27 m R = 29|° maximum polarisation in zenith ; sky clear. 18° 49' 

Babinet. 

7 49 17° 39' 

1843, August 9.— Fine day; rain yesterday. 

Apparent Time. Arago. 

7 h 37 m 19° 34' 

8 3 18 17 

1843, August 10.— Splendid day ; haze in zenith ; slight white cloud's. Barom. 
29-97; hot. 

Apparent Time. 
ll h 38 m R = 24° maximum polarisation in zenith plane. 



POLARISATION OF THE ATMOSPHERE. 



281 



1843, August 19.— Barom. 29-6, falling; haze all forenoon. 

Apparent Time. 
7 51 
7 23 R = 27|° maximum polarisation. 



Arago. 
18° 53' 
18 30 

Babinet. 

17° 50' 



1843, September 6.— Barom. 30 05; splendid, hot day. 

Apparent Time. 

7 h ll m 
7 18 



Arago. 
23° 10' 
Babinet. 

16° 32' 



1843, September 9.— Barom. 3005; fine day. 

Apparent Time. 
6 h 55 m 



Arago. 
19° 25' 

Babinet. 
17° 23' 



1843, September 13.— Barom. 29-98; fine day. 

Apparent Time. 



Arago. 
fiii fim f Neutral point in horizon; R= 25° maximum polar- ) 1f . _., 

\ isation in S. horizon. j 

6 48 Babinet. 

6 53 R= 30° maximum polarisation in zenith , 23J° in S. hor. 16° 26' 



1843, September 20.— Barom. 2980 ; no rain. 

Apparent Time. Arago. 

6 h 14« Clouds W., clear E ; R=23i° zenith, 24|° horizon. 17° 42' 



1843, September 21. — Barom. 30-0, rising 

Apparent Time. 
5 h 46 m 
6 3 
6 28 



Arago. 
fl8° 59' 



r 



5 51 

6 31 



R=.30° maximum polarisation in zenith, 25h° in J 17 55 
horizon ; not a cloud in the sky. > Babinet, 



18 54 
18 43 



1843, September 22. — Barom. 30*28, rising ; thick in horizon, with a brownish 



red light. 



Apparent Time. Arago. 

6 h l m 18° 22' 

6 7 R = 29|° maximum polarisation in zenith, 22£° in hor. 19 58 



1843, October 31.— Barom. 29-39 ; fine sunny day. 

Apparent Time. Arago. 

4 h 9 m 15° 40' 

4 22 17 56 

4 59 20 49 

Babinet. 
4 24 R=29|° maximum polarisation in zenith, 25|-° in hor. 17° 8' 

4 45 Polarisation of moon 24^°. 



282 SIK DAVID BREWSTER ON THE 

1843, November 7.— Barom. 2930, rising; fine day. 

Apparent Time. Arago. 

4 h 29 m R = 29£° maximum polarisation in zenith, 26|° in S. hor. 18° 22' 



1843, November 14. — Barom. 30*13, rising ; fine day ; wind north-west by west. 



Apparent Time. 
4h i2 m 



4 17 R = 28° maximum polarisation in zenith plane. 



Arago. 

18° 33' 

Babinet. 
18° 45 



1843, November 20.— Barom. 29-27, rising ; cold day. 



Apparent Time. 
4 h 36 m 



4 37 



Arago. 
21° 32' 

Babinet. 
18° 13' 



1843, November 29.— Fine day. 



Apparent Time. 
3 h 31 m 



Arago. 
14° 14' 



1 843, December 1 . — Barom. 29-94 ; fine day. 

Apparent Time. 
4 h 10 m 



4 12 



Arago. 
18° 8' 

Babinet. 
19° 26' 



1843, December 6. — Fine day ; wind west ; clear sky everywhere. 



Apparent Time. 
3 h 3 m 



3 7 R = 281°, 90° from sun. 



Arago. 

16° 58' 
Babinet. 
18° 11' 



1844, January 23. — Barom. 27*8, rising; fine day. 



Apparent Time. 
3 h 34 m 



3 37 R=27° maximum polarisation in zenith plane. 



Arago. 
18° 51' 

Babinet. 

17° 31' 



1844, January 25.— Barom. 29-84 ; rain till 2 h p.m. 

Apparent Time. 
4 h 20 m 
4 26 R=28° maximum polarisation in zenith. 



Arago. 
18° 16' 

Babinet. 
19° 0' 



4 38 Polarisation of moon 17 J°. 

1844, February 3. — See " Edinburgh Transactions," vol. xxiii. pp. 220, 227. 



10° 


14' 


14 


33 


15 


31 


Babinet. 


19° 


49' 



POLARISATION OF THE ATMOSPHERE. 283 

1844, February 6. — Snow on ground. 

Apparent Time. Arago. 

3 h 13 m 19° r 

Babinet. 

3 19 R=25° maximum polarisation in zenith plane. 17° 58' 

4 2 R = 27 maximum polarisation in zenith, 19J° in hor. 

1844, February 7 —Clouds over zenith; snow. 

Apparent Time. Arago. 

2 h 18 m 18° 13 

1844, February 16.— Barom. 2974; wind west; fine day. 

Apparent Time. 

12 h 14 m R = 26J° maximum polarisation, to 19£° in horizon. 

1 58 R = 26i „ „ 20* „ 

3 1 R=23| „ „ 181 fj 

Arago. 

3 14 Neutral point in horizon. 
3 20 

3 24 Secondary neutral point in horizon. 

3 33 Sky clouded. 

4 6 Secondary neutral point disappears. 

4 32 

1844, February 21.— See " Edinburgh Transactions," vol. xxiii. p. 220. 
1844, February 27.— Barom. 2912., rising. Thaw. 

Apparent Time. Arago. 

3 h j 6 m Polarisation of moon 17 J°. 

3 44 14° 10' 

1844, March 7.— Barom. 3003, rising. Fine day. 

Apparent Time. Arago. 

4h 4Rm / White nebulosity in zenith; R=13° maximum 1 «q oa/ 
\ polarisation. J 

1844, March 27.— Barom. 29-70, rising. 

Apparent Time. Arago. 

5h 40-m Polarisation of moon 22-|-°. 20 40' 

1844, April 11. — Fine day and fine evening; wind west. 

Apparent Time. Arago. 

6 h 23 m R= 27° maximum polarisation, 221° in horizon. 18° 23' 

7 1 18 37 

Babinet. 

6 24 20° 50' 

7 3 19 19 

VOL. XXIV. PART II. 4 H 



284 



SIR DAVID BREWSTER ON THE 



1844, April 22.— Fine day. Barom. 2980. 

Apparent Time. Arago. 

6 h 29 m R=27£° maximum polarisation, 22£° in S. horizon. 19° 31' 

7 15 20 34 

Babinet. 

6 37 21° 32' 

7 18 R= 28 \° maximum polarisation, 22|° in S. horizon. 17 28 



1844, April 24.— Barom. 2987. Fine day ; windy. 



Apparent Time. 
6 h l m 
6 38 

6 3 



Arago. 
16° 55 
20 30 

Babinet. 
15° 58' 



1844, April 26.— Barom. 2984, rising. 

Apparent Time. 
6 h 24 ra 



Arago. 
19° 20' 



1844, April 27.— Barom. 3007, rising. 

R = 14° 
7 2 A great whiteness in the sky. 



Apparent Time. 
7J1 jm 



Arago. 
20° 50' 
Babinet. 
23° 22' 



1844, May 2.— Barom. 30-25. 



Apparent Time. 
5 h 52 m 
6 

6 33 

7 22 



Arago. 

21° 5' 

R = 15i° maximum polarisation in zenith, 14|° in hor. 22 25 

R=17" „ „ 14 „ 23 20 

R = 20 „ „ 14A „ 22 25 



Babinet. 
13° 40' 



1844, May 3.— See "Edinburgh Transactions," vol. xxiii p. 231. 
1844, May 7.— Barom. 29-80. Whitish sky. 

Apparent Time. Arago. 

7 h 3 m R = 26£° maximum polarisation, 20|° in horizon. 20° 2' 

Babinet. 
7 5 16° 30' 



1844, May 15.— Barom. 30 0, falling. Fine day. 



Apparent Time. 
6 h 36 m 

6 52 

7 46 

6 50 

7 51 



Arago. 

16° 50' 

20 5 

21 40 
Babinet. 
16° 10' 
21 15 



POLARISATION OF THE ATMOSPHERE. 285 

1844, June 3.— Barom. 2986. Wind west. 

Apparent Time. Arago. 

8 h 46 m 20° 58' 

Babinet. 
8 52 20° 35' 

1844, June 10.— See " Edinburgh Transactions," vol. xxiii, pp. 220, 227. 

1844, June 13.— 

1844, August 20. — Barom. 29*77, rising. Fine day. 

Apparent Time. ■ Arago. 

6 h 57 m R=23° maximum polarisation, 27° in horizon. 17° 1' 

7 38 R = 27J „ „ 20 40 

8 8 21 25 
8 46 19 

Babinet. 

8 50 R=29° 17° 15 

1844, August 26. — Barom. 2977, rising. Fine day. 

Apparent Time. Arago. 

6 h 18 m Neutral point among small mottled clouds. 29° 0' ! 

1844, August 29.— Barom. 29-92, falling. Fine day. A China-ink sky. 
Brewster's neutral point distinctly seen. 

Apparent Time. * 

2 h 20 m R = 19£° maximum polarisation in zenith plane. 

1844, September 21. — Barom. 30-1; cold and clear sky. 

Apparent Time. Arago. 

6 h 16 ra R= 28|° maximum polarisation in zenith, 251° in hor. 18° 55' 

Babinet. 
6 18 Polarisation of moon 17 J°. 17° LI' 

1845, January 11. — Fine day, cold ; wind west. 

Apparent Time. Arago. 

2 h 10 m Rzz28J° maximum polarisation in zenith. 8° 15' 

1845, January 20. — Barom. 2948. Fine day ; frosty. 

Mean Time. 

3 h 10 m R = 29° maximum polarisation in zenith. Above Horizon. 

3 15 Alt. of Arago's neutral point, 12" 56' 

3 17 Alt. of Babinet's neutral point ; clouds came on, 22 

1845, January 24. — Barom. 29 -55, rising. 

Mean Time. Above Horizon. 

3 h 37 m Alt. of Arago's neutral point, 11° 0' 

3 59 Alt. of Arago's neutral point, 17 30 

4 4 Alt. of Babinet's neutral point, 19 35 
4 39 Alt. of Arago's neutral point, 13 35 
4 41 Alt. of Babinet's neutral point, 24 



286 ON THE POLARISATION OF THE ATMOSPHERE. 

1845, January 31— Therm. 18° at 10 h p.m. of the 30th; 8 h a.m., therm. 12°. 
Barom 2954. rising. Fine frosty, clear day ; ground covered with snow. 

Mean Time. 

12 h 55 m R = 26|° in zenith and in horizon. 

12 55 Arago's neutral point in N, hor. ; sun's alt. then 14° 45'. 

1 40 Arago's neutral point still in horizon. 

1 40 R = 26|-° in zenith. 

1845, February 1.— Barom. 2980. Frosty day; cloudy till 3 h . 

Mean Time. Above Horizon. 

3 h 30 m Alt. Arago's neutral point, 8° 15' 

R=20J° maximum polarisation in zenith to 14|° in hor. 
3 45 Alt. Arago's neutral point, 14 30 

R=22^° maximum polarisation. 

1845, April 8.— Barom. 2906. 

Mean Time. Above Horizon. 

5 h 35™ Alt. Arago's neutral point, 9° 10' 

6 1 „ „ 20 20 

5 39 Alt. Babinet's neutral point, 25 10 

6 4 „ „ „ 15 25 

1845, April 15.— See " Edinburgh Transactions," vol. xxiii. p. 220. 
1845, July 14. — On the top of Scuirmore, near Glenquoich. 

Mgan Time. Above Horizon. 

5h 24 m Altitude of Arago's neutral point, 6° 40' 

R = 23|° maximum polarisation in zenith plane. 

1845, September 6. — Barom. 30-10. Fine day; a milky sky. 

R=17° maximum polarisation in zenith plane. 

Above Horizon. 

R = 23° Arago's neutral point. 11° 0' 

Arago's secondary neutral point seen in horizon. 13 24 

Arago's neutral point, 19 10 

Babinet's R = 28^° maximum polarisation, 24° in ( 24 

horizon. \ 20 24 

1850, July 1, 15, 29.— See " Edinburgh Transactions," vol. xxiii. p. 237. 
1850, July 9. — Barom. 29-79, rising. Fine clear sky. 

Mean Time. 
6 h 56 m Bands just visible at the land horizon. 

7 5 Bands invisible close to land horizon. 

7 21 During the previous 21 minutes no trace of the + 

bands was seen. At 7 h 21 m they were seen, and 
became rapidly brighter. 

The positive action which here produced the secondary neutral point was not 
strong enough to produce it by exhibiting the + bands counteracting the — ones, 
at some height above the horizon ; but it was strong enough to neutralise them 
for 21 minutes, and to weaken them greatly when they did appear. 



Mean Time 


l h 


10 m 


5 


31 


5 


41 


6 


36 


5 


43" 


6 


28 



( 287 ) 



XXII.— On the Laws of the Fertility of Women. By J. Matthews Duncan, M.D. 

(Bead 6th February 1866.) 

In a former paper* I described the variation of the fecundity of women 
according to age, and arrived at the conclusion that the climax of fecundity in 
women was at or near the age of 25 years. Researches, completed since that 
paper was read, regarding the variations of length and weight of children accord- 
ing to the mother's age, and regarding the mortality of childbed as influenced by 
the mother's age, have been published in the " Edinburgh Medical Journal." The 
results of these investigations seem to illustrate and confirm the statement made 
as to the age of the climax of fecundity, for I have found that, about that age, women 
produce the bulkiest children, as measured by length and weight ; and about the 
same age of the mother there is the smallest mortality in childbed. As still 
further adorning the age of 25, I may add, that several sets of observations, 
including some made in St George's-in-the-East, London, and published in the 
eleventh volume of the "Journal of the Statistical Society," show a greater amount 
of survival and rearing among children born of women about that age than at any 
other ; and recently Dr Arthur Mitchell has published a collection of cases of 
idiocy, with the respective ages of the mothers at the time of the idiots' births, 
and these also show a smaller proportion born of women about the age of 25 
years than at greater and lesser ages.f 

In the last portion of the paper first alluded to, having described initial fecun- 
dity, the age at which women are most likely to beget children soon after marriage, 
I said that I could not advance further without encroaching on another topic, viz., 
the fertility of marriage ; or, as marriage is scarcely admissible as a term in phy- 
siology, the subject may be designated " sustained fecundity," or the laws of the 
fertility of women cohabiting with men during the child-bearing period of life. 
It is this subject which I propose here to enter upon. So far as I know, very 
little is ascertained or known in this department of physiology. The writings upon 
it are for the most part to be found in the works of political economists, and are 
chiefly confined to the single question of the rate of increase of a population under 
varying circumstances. To illustrate this topic, which is one of little interest to 
the physiologist, data are numerous and abundant. But when the writers re- 
ferred to attempt to go deeper into the fundamental laws of the fertility of 
women, having very scanty materials and using them without care, they arrive at 
scanty results, which are either positively erroneous or of little value. 

* Trans. Roy. Soc. of Edinburgh, vol. xxiii. p. 475, &c. 
•J 1 Edinburgh Medical Journal, January 1866. 

VOL. XXIV. PART II. 4 I 



288 DR MATTHEWS DUNCAN ON THE 

" The statistics," says Mr Graham, registrar-general for England, " of a coun- 
try in which the age of a mother at marriage, and at the birth of her children, is 
not recorded, must always remain imperfect, and leave us without the means of 
solving some of the most important social questions."* These data were secured 
for the first year of the registrations in Scotland. The results to be now described 
are derived from a study of a part of these registers, namely, those of Edinburgh 
and Glasgow for 1855, and are founded on an analysis of 16,301 families of wives. 

Chapter I. — The Fertility of the whole Marriages in a Population. 

On this subject much has been written, in latter times chiefly by Malthusians 
and anti-Malthusians, to whose works I refer generally. Elaborate comparisons 
are made between the fertilities of marriage in different countries ; and there are 
exhibited variations to so great an extent, that they appear themselves to show 
the worthlessness of the data and of the comparisons instituted, at least in a 
physiological point of view. In illustration, I may refer to the variations described 
by M. Benoiston de Chateauneuf,t in a paper on the intensity of fecundity in 
Europe at the commencement of the nineteenth century. The highest figure is 
derived from some villages in Scotland, where there are asserted to be six or seven 
children to a marriage, while his lowest figure is 2*44, the alleged productiveness 
of marriages in Paris. 

We shall restrict our view to Great Britain, and we find the method generally 
followed of estimating the fertility of marriage to be the very old and simple one of 
dividing the number of legitimate births in any year by the number of marriages. 
" In 1861," says Dr Stark,:}: " for every marriage which occurred in Scotland there 
were born 4'64 legitimate children ; that is to say, 464 legitimate children were 
born to every 100 marriages. During the same year, in England, only 389 legi- 
timate children were born to every marriage, or 389 legitimate children to every 
100 marriages." This is an exemplification of the ordinary method of calculating, 
and it is evident that the result derived is of not the slightest value as a contri- 
bution to the science of fertility. For, besides including marriages of all dura- 
tions and at every fecund age, also second and third marriages, it includes many 
marriages at ages when fertility has entirely disappeared. It is impossible, in- 
deed, to state what is the exact relation between the number of marriages in a 
population in any year and the number of legitimate children born in the same 
year, with a view to any physiological result. This aspect of the statement is, 
however, well worthy of being pointed out, because authors of respectability, 
whom it is needless to name, refer to and use these figures as exhibiting the fer- 

* Registrar-General's Report for 1845, p. 14. (England). 

■f Annales des Sciences Naturelles, tome ix. 1826. 

\ Seventh Detailed Annual Report for 1861, published in 1865, p. xviii. (Scotland). 



LAWS OF THE FERTILITY OF WOMEN. 289 

tility of continued married life in England and Scotland. Malthus was well 
aware of the real meaning of these figures, — of the fact that they merely show the 
relative frequency of marriage ceremonies and births in a population. " The rule," 
he says,* " which has been here laid down, attempts to estimate the prolificness 
of marriages, taken as they occur; but this prolificness should be carefully distin- 
guished from the prolificness of first marriages andof married women, and still 
more from the natural prolificness of women in general, taken at the most favour- 
able age. It is probable," he adds, "that the natural prolificness of women is 
nearly the same in most parts of the world ; but the prolificness of marriages is 
liable to be affected by a variety of circumstances peculiar to each country, and 
particularly by the number of late marriages." 

As a corollary from the preceding data, of value only in proportion to their 
value, it may be stated that the average duration of fertility in married women 
(including those who do not bear children) is about 7\ years. For, as the inter- 
vals between marriage and the birth of a child, and between the births of succes- 
sive children, is, on an average, 20 months, and as there are about 4| children to 
each marriage, we have about 7| years, counting from marriage, spent in pro- 
ducing that number. 

British authors, as Graunt, Short, Malthus, Sadler, Senior, and those of 
later date, name 4, 4 J, or 5, as the fertility of marriage. Malthus, founding on such 
data, gives a wife eight years of fecundity to produce four children, a statement 
which cannot be passed over without the obvious remark that Malthus, so calcu- 
lating, utterly neglects the force of the wise words which we have just quoted 
from his work. 

I have nothing satisfactory to offer as to prolific marriages, to contrast with 
the statements given concerning all marriages. Dr Lever f says, that " the ave- 
rage number of children consequent upon a prolific (not every) marriage is shown 
to be rather more than 5f , but not amounting to 6." This is given without any 
authority stated or evidence detailed, and I know not what value to ascribe to it. 
In a physiological point of view, its value must be scarcely appreciable ; for no 
allowance is made for the duration of the marriage, nor for the age of the woman 
at the time of the ceremony. 

In St George's-in-the-East, London, the average number of children consequent 
on the prolific marriages was 5 to each marriage. $ That is, 5 is the average 
number of children that has been born in all the families in a place at a given 
time. It tells nothing concerning the average number in completed families, or in 
still-growing families. § 

* Essay on the Principle of Population, vol. ii. p. 6. 
t On Organic Diseases of the Uterus, p. 5. 

% Quarterly Journal of the Statistical Society of London, vol. xi., 1848. 

§ Some interesting facts regarding the fertility of Esquimaux women are to be found in 
Roberton's " Essays and Notes on Physiology and Diseases of Women," p. 53. 



290 DR MATTHEWS DUNCAN ON THE 

Franklin says, that the females in America have, " one with another, eight 
children to a marriage;"* almost certainly a great exaggeration, especially as 
he does not even state, as a condition, that the marriages were prolific. 



Chapter II. — Annual Fertility of the Married Women of Child-bearing Age in 

a Population. 

Seeing the inexactness of the statements of which those just given are an 
example, Dr Stark has adopted another method of arriving at the comparative 
prolificness of marriages in England and Scotland. " In 1861," says he, " when 
the census was taken in England, the numher of wives at the child-hearing ages, 
viz., 15 to 45, was 2,319,049 ; and as the numher of legitimate children horn 
during the year amounted to 652,249, this gives the proportion of one legitimate 
child for every 355 wives at the ages 15 to 45 in the population ; or, in other 
words, every 355 wives in England, at these ages, gave birth to 100 children 
during the year. In Scotland, during the same year, there were 305,524 wives 
between the ages of 15 and 45 years ; and as 97,080 legitimate children were horn 
during the year, this gives the proportion of one legitimate child for every 3 14 
wives at these ages in the population; or, in other words, every 314 wives in the 
population of Scotland, at these ages, gave birth to 100 legitimate children during 
the year." 

While for every marriage in 1861 there were born in the same year in Scot- 
land 4-64 legitimate children ; every 3-15 wives between 15 and 45 in Scotland in 
the same year produced one legitimate child. Of 54,408 wives in Edinburgh and 
Glasgow in 1855 between 15 and 44 years of age, inclusive, 16,290 bore children 
fit for registering; or, 1 child was born to every 3 3 wives aged from 15 to 44. 

If we adopt these latter statements, we must take care to note that they 
do not give the fertility of the whole marriages in a population, as the older and 
former statements in chapter first do. These latter give the annual productive- 
ness of a mass of married women in our populations. The results of the two 
methods of computing the fertility of marriage cannot be contrasted, for each is 
concerned with an entirely different topic from the other. 

Chapter III. — The Fertility of the whole Marriages in a Population that are 

Fertile at a given time. 

In Edinburgh and Glasgow in 1855 there were 16,393 wives who bore first 
or subsequent children. Of these the necessary data are given in 16,301 cases 
These 16,301 mothers had produced 60,381 children; or 37 children constituted 

* Sadler. Law of Population, vol. ii. p. 495. 



LAWS OF THE FERTILITY OF WOMEN. 



291 



the average production of each mother. In other words, excluding the large class 
of wives sterile in 1855, we have 3 7 as the average number of children (surviving 
or not surviving) in each family that increased in 1855. 

To compare with the above result, we may observe 16,414 women delivered in 
the Dublin Lying-in Hospital during Dr Collins' mastership, who had borne 
53,458 children, whose families, on an average, numbered 3 25 ; also 6634 women 
delivered in the same hospital during the period reported on by Drs M'Cltntock 
and Hardy, who had born 20,680 children ; whose families, on an average, num- 
bered 3 12. 

As there can be no doubt that these 16,301 families are a fair sample of all 
the growing families in Edinburgh and Glasgow, it appears that the average size 
of growing families existing at a particular time in our population is between 3 
and 4 ; and, if it be true that, on an average, children are born with an interval 
not exceeding twenty months, then all mothers child-bearing at any particular 
time have been on average less than seven years fertile. It is to be remarked, 
that this statement concerns only the families of wives mothers child-bearing at 
a particular time (i.e. in 1855), and is not to be compared with the corollary to 
Chapter I., which includes all families, and especially the mass of completed 
families. 

The accompanying Table (I.) shows the data upon which these statements are 
founded. It, in addition, gives the percentage of children (surviving or not) in 
families of different numbers, that increased in 1855. 



TABLE I. — Showing the Number and Percentage of Mothers Bearing respec- 
tively 1st, 2d, and 3d Children, and so on ; also Percentage of Children in 
Still-Growing Families of Different Numbers. 



Number 


Number of 


Percentage 


Percentage 


Number 


Number of 


Percentage 


Percentage 


of 


Wives 


of Wives 


of 


of 


Wives 


of Wives 


of 


Child. 


Mothers. 


Mothers. 


Children. 


Child. 


Mothers. 


Mothers. 


Children. 


1 


3,722 


22-83 


6-16 


11 


152 


•93 


2-77 


2 


2,893 


17-74 


9-58 


12 


61 


•37 


1 21 


3 


2,534 


15-54 


12-59 


13 


34 


•20 


•732 


4 


1,982 


12-16 


13-13 


14 


11 


•06 


•255 


5 


1,543 


9-46 


12-77 


15 


6 


•03 


•149 


6 


1,221 


7-49 


1213 


16 


2 


•01 


•053 


7 


848 


5-20 


9-83 


17 


2 


01 


•056 


8 


641 


393 


8-49 


18 


1 


•006 


•029 


9 


425 


2-60 


6-33 


19 


1 


•006 


031 


10 


222 


1-36 


367 











VOL. XXIV. PART II. 



4 K 



292 DR MATTHEWS DUNCAN ON THE 

Chapter IV. — The Fertility of Fertile Marriages lasting during the whole 

Child-bearing Period of Life. 

This subject may be stated in the form of a question. How many children 
does a fertile woman produce, living in wedlock from 15 to 45 years of age? The 
only collection of data known to me, which can throw light on this point, is that 
published in the "Report to the Council of the Statistical Society of London, from 
a Committee of its fellows, appointed to make an investigation into the state of 
the poorer classes in St George's-in-the-East." * In that district there were found 
80 mothers married at ages varying from 15 to 19, and who had lived in wed- 
lock at least 31 years. These fertile wives having lived nearly all the child- 
bearing period of life in wedlock, had borne on an average 9-12 children. 

There are evident sources of inexactness in the above very limited data, 
which tend to diminish the average fertility ; and it will be as near the truth 
to state 10 as the average fertility of fertile marriages lasting during the whole 
child-bearing period of life. 

The conclusions given in further parts of this paper will show that the figure of 
10 children, for 30 years of child-bearing life, is Dot indicative of each mother 
having borne a child every third year. The fertility, while it lasts, will be shown 
to be much intenser than this. The average interval between births of living 
children is hereafter shown to be 20 months, which gives about 17 years as the 
average duration of fecundity in a fertile woman living in the married state all 
the child-bearing period of life. 

In his work on Abortion and Sterility, Dr Whitehead gives no data which I 
can properly collate with those just given. After stating his belief that the actual 
duration of the child-bearing period in the female of this climate is about 20 
years, he adds, that a woman, under favourable circumstances, has in that 
period 12 children. But as this includes abortions and premature deliveries, 
which he estimates at 1^ for each individual, the figure 12 has to undergo that 
reduction for comparison with 10, and the approximation is very close. 

Sadler states as a fact, " that marriages, on the average, are only fruitful for 
about a third part of the term of possible fecundity. f" But he nowhere, so far 
as I know, affords any evidence of this statement, and I therefore attach to it no 
importance. 

* Quarterly Journal of the Statistical Society, August 1848, vol. xi. 
t Law of Population, vol. ii. p. 276. 



LAWS OF THE FERTILITY OF WOMEN. 293 

Chapter V. — The Fertility of Persistently Fertile Marriages lasting during 
the whole Child-bearing Period of Life. 

This subject may also be conveniently stated in the form of a question. How 
many children does a fertile woman produce, living in wedlock from 15 to 45 
years of age, and bearing children periodically up to the end of that time ? 

To this question I cannot give at once an answer founded on sufficient data ; 
and I shall invert my usual mode of proceeding, stating the conclusion, namely, 
that 15 at least is the average number of children borne by a persistently fertile 
female in 30 years, before giving the reasons for it. These are as follows: — 
A persistently fertile woman, at all ages, is found to have borne one child about 
every 2 years ; the average fertility of 15 mothers who have had each 26 years of 
persistently fertile life is 13. The fourth Table, to be hereafter given, showing an 
excess of fertility on the part of those long persistently fertile, or bearing children 
in the year of counting, would give 16 as the proportional fertility of 30 years of 
persistently fertile marriage, calculating from the actual values given for the 
other results in the Table. The deficiency of actual facts for settling this point is 
to be seen in the next Table (II.), where the number of women bearing children 
when above 26 years married, is only 7. 

On this subject Allen Thomson makes the following statement, which is 
remarkably accurate, seeing that it is apparently not founded on any analysis of 
documents. "A healthy woman," says he,* "bearing during the whole time, 
and with the common duration of interval, may have in all from 12 to 16 
children, but some have as many as 18 or 20." 



Chapter VI. — Fertility of Persistently Fertile Wives at different Years of 

Mar?*ied Life. 

The following Table (II.), from the 1855 Edinburgh and Glasgow data, gives 
at a glance the rate of yearly increasing production of wives mothers who are 
still fertile — that is, who produced a living child in the year of our census or 
counting. It is framed by adding together the whole children born of mothers 
having different durations of marriage, and dividing the sum by the number of 
mothers corresponding to each duration of marriage. The results will be found, 
on the whole, to tally pretty closely with those given in Table VI. It is easy to 
account for the differences between the two Tables. In the latter Table the wives 
arrived at different numbers of progeny are collated and compared, while in the 
former the wives arrived at different durations of marriage are collated and 
compared. The Table requires no further explanation ; it is easily read. 

* Todd's Cyclopsedia of Anatomy and Physiology, vol. ii. p. 478. 



294 



DR MATTHEWS DUNCAN ON THE 



TABLE II. — Showing the Average Number of Children that have been Born 
at the Completion of each Year of Persistently Fertile Marriage. 





Number of 


Number 


Average to 


Duration of Marriage. 


Wives 


of 


each 




Mothers. 


Children. 


Mother. 


1 year married and under, 


16,301 


60,381 


370 


3,172 


3,336 


1-06 


2 years 


1,223 


2,090 


1-70 


3 „ 55 


1,540 


3,195 


2-07 


4 

^ 55 55 


1,248 


3,229 


2-58 


5 „ ,5 


1,193 


3,645 


305 


6 ,5 55 


1,122 


3,959 


3-53 


7 „ 


870 


3,414 


3-92 


8 „ „ 


733 


3,225 


4-40 


" 55 55 


719 


3,447 


4-79 


10 „ 


761 


4,021 


5-28 


11 „ 


624 


3,502 


5-61 


12 „ 


520 


3,134 


6-03 


13 „ 55 


441 


2,878 


6-53 


14 „ 


393 


2,698 


686 


15 5) 55 


372 


2,659 


715 


16 ,, „ 


293 


2,248 


767 


17 „ 


240 


1,918 


7-99 


18 „ „ 


198 


1,647 


832 


I" 55 55 


177 


1,541 


8-71 


20 „ 


142 


1,303 


9-17 


21 „ 


115 


1,116 


9-70 


22 „ 


80 


790 


9-87 


23 „ „ 


56 


557 


9-95 


24 „ 


39 


415 


10 64 


25 „ 


8 


95 


11-87 


26 „ 


15 


195 


1300 


27 „ 


2 


25 


1250 


28 „ 


3 


42 


14 00 


■^" 55 55 


1 


14 


1400 


30 „ 


1 


13 


1300 



Chapter VII.— Fertility of Fertile Wives at Different Periods of Married Life. 

With a view to comparison with the results given in Table II., I have prepared 
the following Table (III.), from the data of St George's-in-the-East, already 
referred to. The circumstances in which these data were collected, and their pau- 
city, do not justify me in ascribing to them a value equal to those given in Table 
II., nor do I think they are well adapted for the purpose of the comparison for 
which they are adduced. But I know no other to refer to. 

As in the Report of the Committee of the Statistical Society, the periods are 
counted from the birth of the first child, I have added to them 17 months (l T \ths 
year), the average interval between marriage and birth of a first child, with a 
view to make the Table more easily contrasted with Table II. 



LAWS OF THE FERTILITY OF WOMEN. 



295 



TABLE III. — Showing, from the data of St George's-in-the-East, the Fertility 
of Fertile Wives Aged from 15 to 45 Years. 



Years 
Married. 


Motliers. 


Children. 


Average of 
each Mother. 


Years 
Married. 


Mothers. 


Children. 


Average of 
each Mother. 


** 


56 


59 


1-05 


8 s - 

"1 2 


76 


269 


354 


3 A 


60 


88 


146 


ll- 6 - 


254 


1,178 


4-64 


*A 


54 


99 


1-83 


16- 5 - 

lu 12 


215 


1,319 


6-13 


5 6 


66 


184 


2-79 


21 T 5 2 


148 


1,075 


7-26 


6- 5 - 


57 


163 


2-86 


26A 


44 


353 


8-02 


7VW 

« 12 


60 


196 


326 











The direct results of this Table are given in the figures, and require no state- 
ment. But comparing it with the preceding Table, we observe that, as is easily 
understood, the differences between the fertile and the persistently fertile increase 
as the duration of marriage increases ; and that, while the numbers of the children 
of fertile women is about a third of the years of duration of marriage, the numbers 
of the children of persistently fertile women is about a half of the years of dura- 
tion of marriage. In other words, if these Tables are at all trustworthy, we may 
guess that the number (surviving or not) of a fertile married woman's family is 
about a third of the number of years since her marriage. But if, in addition to 
knowing that the married woman has a family, we know that she has just had 
an addition to her family, then we may guess that the number of her family is 
about a half of the number of years since her marriage. 

From the same London data I have also framed the following Table, without 
doing any apparent violence to them, and with a result that is extremely interest- 
ing. The student will observe, that beside the data from St George's-in-the-East 
I have placed corresponding data extracted from the Edinburgh and Glasgow 
registers of 1855. The comparison of the fertility of a set of fertile wives — that 
is, all wives who have borne children some time during their still-continuing mar- 
ried lives — with that of a set of persistently fertile wives — that is, exclusively, 
of wives bearing at the ends of the periods under consideration (that is, in this 
Table, the end of their child-bearing lives) — is, as already said, marred, and loses 
value on account of the two sets being of very different numbers, different locali- 
ties, and different populations. Taking it as it stands, we find that fertile women 
generally, living with husbands for 16 years before the conclusion of child-bearing 
life, have an average family of about 41 ; while persistently fertile wives — that is, 
wives bearing children at the end of their child-bearing lives — have an average 
family of Hi. While fertile wives, married 21 years, before and up to the age of 

VOL. XXIV. PART I. 4 L 



296 



DR MATTHEWS DUNCAN ON THE 



45, have an average family of about 6 ; persistently fertile wives have an average 
family of 104. While fertile wives married for 26 years, before and up to the age 
of 45, have an average family of 8 ; persistently fertile wives, in the same circum- 
stances, have an average family of about 14. While fertile wives, married for 31 
years, before and up to the age of 45 years, have an average family of 9 ; per- 
sistently fertile wives, in the same circumstances, have an average family which 
may be estimated at 16. 

TABLE IV. — Showing a Comparison of the Fertility of Mothers and of 
Persistently Fertile Mothers. 



Age at 
Marriage. 



15-19 
20-24 
25-29 
30-34 



Duration 
of Marriage. 



At least 31 yrs. 
At least 26 yrs. 
At least 21 yrs. 
At least 16 yrs. 



(St George's-in-the-East.) 



Wives Mothers. 



Number of 
Mothers. 


Number of 
Children. 


80 


730 


179 


1418 


100 


630 


25 


115 



Average 

fertility of 

each Mother. 



912 
7-92 
630 
4-60 



(Edinburgh and Glasgow in 1855.) 

Wives Mothers bearing Children at 
the end of Child-bearing life. 



Number of 
Mothers. 



Number of 
Children. 



83 
74 

46 



Average 

fertility of 

each Mother. 



16 

13-83 
10-57 
11-50 



In this Table (IV.) it will be observed that the differences between the fertile 
and the persistently fertile are much greater than in the former (II. and III.), a cir- 
cumstance which is easily explained. For, in the latter, all the women have been 
long married, and the persistently fertile have had time to far outrun the average 
fertility of all the fertile. It must also be noted, that all the women in the Table 
are fertile at or near the end of the child-bearing period, a time at which, it will 
be hereafter shown, the intensity of fertility is greater than at any other. 



Chapter VIII. — Degrees of Fertility of Wives Mothers of Families of different 

Numbers. 

Under this head, the first question that raises itself relates to the interval 
between marriage and the birth of the first child. In Table V. this question is 
found fully answered. In fertile marriages generally, there intervene about 
17 months (1-38 year) between the ceremony and the birth of the first child. 
But in women of all ages this interval is far from being identical. As age 
increases above 25 years, the interval increases; the hope of the female is 
longer of being realised. The Table does not confirm this statement for wives 
married at 40 and upwards ; but this is almost certainly a mere result of the 
paucity of the data at these ages. The whole tenor of the Table confirms the law 
of greatest fecundity according to age, meaning by fecundity, likelihood of having 



LAWS OF THE FERTILITY OF WOMEN. 



297 



children. For it is observed, that not only are wives most fecund from 20 to 24, 
but also that they begin the career of fertility sooner than their younger or elder 
sisters. 



TABLE V. — Showing the Interval between Marriage and the Birth op a 
First Child in Wives Married at Different Ages. 









Mother's 


Age at Marriage. 


























Total. 


15-19. 


20-24. 


25-29. 


30-34. 

• 


35-39. 40-44. 


45-49. 




1 Less 


94 


325 


126 


44 


15 


4 




608 




1 


409 


1,259 


533 


135 


49 


3 


2 


2.390 




2 


83 


202 


88 


45 


17 


2 


* • • 


'437 




3 


25 


50 


35 


12 


10 


1 




133 




4 


8 


31 


13 


8 


1 


... 




61 




5 


13 


10 


3 


3 


3 






32 


. 


6 


5 


14 


6 


1 


1 






27 




7 


5 


3 


1 


3 




... 




12 


u 

S3 


8 


1 


3 


1 


... 




, . . 




5 


S 


9 


2 


3 








, , 




5 


CO 

- 


10 


• • • 


1 








, . , 


• • . 


1 


S3 


11 




1 


2 










3 


&H 


12 
13 


2 
1 


1 
1 


1 




... 




... 


4 
2 




14 












■ • • 




• • • 






15 


1 








• i • 


• • • 


. . 


• • • 


1 




16 




... 










, . 


■ • . 






17 














.. 


■ » • 


• * • 


\ 


18 




1 






... 


... 


•• 


... 


1 




| Total 


649 


1,905 


809 


251 


96 


10 


2 


3,722 


Average inter- 




















val between 


Year. 


1-516 


1-329 


1-350 


1-510 


1-594 1- 


400 


1-000 


1-385 


Marriage and 




or 


or 


or 


or 


or ( 


>r 


or 


or 


Birth of first 
Child. 


Months. 


18-2 


15-9 


16-2 


18-1 


19-1 1 


6-8 


120 


166 



It is noteworthy, that while the average interval between marriage and the 
birth of the first child is 17 months, the average interval between the births of 
successive children, however numerous, is a little under 20 months ; the two 
intervals approximating one another so closely as to destroy all probability of 
the truth of the explanations usually offered for the delay of impregnation after 
a recent childbirth, and of the efficacy of continued lactation in retarding the 
occurrence of a new conception. And we shall soon see, in a quotation from 
Sadler, that he finds that women who do not suckle their offspring have as long 
an interval between conceptions as others. But, while Sadler by this demonstra- 
tion destroys the only foundation for his invective against the rich who do not 
suckle, he nevertheless proceeds enthusiastically, as if the dictum of physiologists 
were valid, even after their argument was ruined. 



298 



DR MATTHEWS DUNCAN ON THE 



Speaking of the interval between marriage and a first birth, Sadler* gives the 
following indefinite statement: — "Married females do not become fruitful, on 
the average, during the first year of their nuptials, but nearly so. A great 
number of cases which I have collected, with a view of determining this point, 
give three-fourths of them as producing their first child at the average of one year 
after marriage." 

Whitehead,! founding on the observation of 541 married women, of the 
average age of 22 years, makes out the average interval between marriage and 
the birth of a first child, to be 1L| months. 

Quetelet^: admits, with sufficient probability, as an average term, that the 
birth of the first-born takes place within the first year which follows marriage. 
His error, as those of the others, depends on the acknowledged want of docu- 
ments. 

It next comes to be inquired at what rate children succeed each other in 
families. This interesting topic is developed from the data given in Table VI. 
It is formed by dividing the whole years of duration of sets of marriages, of dif- 
ferent durations, by the number of children born in the corresponding marriages ; 
and it must be remembered, that as our data all spring from women who were 
fertile on the year of our census or counting, no women are included who, although 
fertile formerly, have now ceased to be so ; and it is evident that, for the purposes 
of our argument, this is just. 

TABLE VI. — Showing the Average Duration op Marriage at Birth of each Suc- 
cessive Child ; and the Average Interval between the Births of the Succes- 
sive Childken.§ 



Number 

of 

Child. 


Number 

of 
Mothers. 


Duration of 

Marriage 

in Months. 


Average interval 
between suc- 
cessive Births. 


Number 

of 
Child. 


Number 

of 
Mothers. 


Duration of 

Marriage 

in Months. 


Average interval 
between suc- 
cessive Births. 


1 

2 
3 
4 
5 
6 
7 
8 
9 
10 


3,722 

2,893 

2,534 

1,982 

1,543 

1,221 

848 

641 

425 

222 


17 

38 

64 

90 

115 

137 

162 

181 

203 

225 


17-0 
190 
21 3 
22-5 
230 
228 
231 
226 
22-5 
225 


11 
12 
13 
14 
15 
16 
17 
18 
19 


152 
61 

34 

11 

6 

2 

2 

1 
1 


235 
246 
263 
281 
280 
336 
252 
252 
204 


214 
20-5 
202 
20-1 
18-7 
210 
148 
14-0 
10-7 


Average 


19-9 



**The Law of Population, vol. ii. p. 30. f On Abortion and Sterility, p. 242. 

J Treatise on Man, p. 15. 

§ This is not a correct statement of the contents of this Table. The last column does not 
directly give the average interval between the births of successive children, but the average interval 
between marriage and the birth of the child, divided by the number of the children born. For 
brevity's sake, the title is left as it stands. 



LAWS OF THE FERTILITY OF WOMEN. 299 

The first conclusions deducible from the data are : — 

1. That the mass of early or first children, up to the third or fourth, come into 
the world in more quick succession than those that immediately follow. 

2. That a mass of children, numbering from the fourth or fifth on to the 
tenth, succeed one another more slowly than those of the first category, and of 
the third. 

3. That a mass of children, following the tenth, come into the world hurrying 
after one another with a gradually increasing rapidity, which excels that of all 
their predecessors (a circumstance which may, in part at least, account for the 
great mortality of women bearing children after the ninth.)* 

While all these propositions are true of a large number of children, it must 
not be supposed that they directly indicate laws regulating the fertility of women. 
But the Table bears important information relative to this last topic. And 
it appears to me that the first of the three conclusions given above can be 
explained only by supposing what may therefore be held as equally well demon- 
strated : — 

1. That wives bearing their early children up to the third or fourth, breed 
more rapidly than they subsequently do. 

For the average fertility of all wives is at least 4 children ; and the great mass 
of fertile wives is therefore included in the calculation. All the wives destined to 
bear large families, and furnish data for the second and third conclusions, are in- 
cluded in the data for first 4 children. The mass of children born in families num- 
bering 10 and more, is not large enough to have great influence on the data, should 
it be the case that they are proportionately very quick breeders from the first. 

If we now regard the mothers whose children have afforded the data for the 
second conclusion as to the rapidity of the succession of a mass of children, we 
shall have, I think, no difficulty in accepting the proposition, — 

2. That wives produce their children, numbering from the third or fourth on 
to the tenth, at greater intervals than their earlier progeny. 

For, in the calculations, the earlier and more rapidly succeeding progeny are 
included, and have their full influence, and diminish the periods given in the Table 
opposite children numbering from 4 to 10, reducing them below what they would 
be were pregnancies from 4 to 10 alone counted, exclusive of those from 1 to 4. 

Regarding, now, the mothers of families numbering 11 or more, it is evident 
that their paucity, though not such as to destroy all their value, is such as to 
prevent their having a paramount influence upon the figures of the two preceding 
categories. It might therefore appear necessary to leave undecided whether 
their specially rapid bearing were a consequence of their great fertility, and there- 
fore an acquired or secondary rapidity, or were an original condition true of even 

* Edinburgh Medical Journal, September 1865, p. 209. 
VOL. XXIV. PART II. 4 M 



300 DR MATTHEWS DUNCAN ON THE 

their earlier pregnancies. That the latter is to be accepted to the exclusion of the 
former supposition is evident, if we observe that the married life of the women 
with families above 10 is not long enough to admit of their having gone through 
the series of lengths of pregnancies given in the Table opposite each successive 
child. It is thus shown, — 

3. That wives bearing more than 10 children, or wives bearing very large 
families, breed more rapidly than others during their whole child-bearing lives. 

Wives, therefore, who bear numerous progeny, do so in virtue of two differences 
from other married women. They bear their children more rapidly, and they 
continue fertile longer than their neighbours. 

Were the third conclusion just given not before us, it might be supposed that 
the rapid bearing of earlier children was a result of youth and vigour. This 
supposition is not only inconsistent with the third conclusion, but with the law 
to be hereafter demonstrated, that the oldest women, who are continuedly fertile, 
bear children more rapidly than any other. 

The average length of interval between all successive children is (1 09;, nearly 
20 months. 

I have frequently heard it said, that a fertile woman bears a child every 2 
years. Some authors have made careful statements on this point. Whitehead* 
says, that fertile women produce children every 20 months ; but " this in- 
cludes abortions, false conceptions, so-called premature deliveries, and all having 
an unsuccessful issue, the average amount of which will be rather more than one- 
and-a-half for each individual." Sir William Petty long ago laid it down, that 
" every teeming woman can bear a child once in 2 years." Malthusj adopts 
the same period, and refers to the Statistical Account of Scotland as confirming 
it. The number and exactness, however, of the data here adduced, and the cir- 
cumstance that they include only children born alive (excluding still-born and 
abortions), leave no room for doubt that all the authors referred to under- estimate 
the rate at which married women bring children into the world.} 

On this point Sadler is so full and distinct that I quote his words. " The 
interval of time," says he, " at which the fruitful couples produce their children, 
calculated from the period of their marriage to the birth of their last child, in- 
cluding the greater prolificness of the first year, exceeds 2 years. It extends to 
between 2^ and 2^ years, if calculated from the first birth. "$ In this calcula- 
tion, as in that of the interval between marriage and the birth of a first child, 
Sadler evidently errs, making the former too long, and the latter too short. 
For both he gives no data ; yet, in regard to the interval between the births of 

* On Abortion and Sterility, p. 245. 

f An Essay on the Principle of Population, vol. ii. p. 3. 

+ See also Roberton's Essays and Notes on the Physiology and Diseases of Women, p. 185 

§ Vol. ii. p. 30. 



LAWS OF THE FERTILITY OF WOMEN. 301 

successive children he says : — "All the Tables are constructed upon the pre- 
sumption of its certainty, and, happily, it is one which, on this very debatable 
question, has never been made the subject of controversy, and which does not 
admit of it. Nothing," he continues, " is more certain, or better ascertained, than 
the average period at which the human female, in a state of prolificness, repro- 
duces. Were we, indeed, to form our general rules from particular exceptions, 
we should in this, as in all other cases, be grievously misled ; we might conclude, 
for instance, that she would continue to multiply within the year; but general 
computations will rectify any such error, and conduct us to conclusions which 
are not only reconcilable with philosophy and truth, but resolvable into the 
ordinations of a merciful Providence. The human mother has to feed her infant 
for a period pretty nearly corresponding in length to that of gestation (I speak 
now as regards the necessity of the great mass of the community, with whom 
the question evidently rests) ; nature, therefore, has kindly ordained, as a general 
rule, that the period of impregnation shall be postponed till that essential duty is 
discharged, and for a period somewhat beyond it ; and he must be ignorant 
indeed, who does not see most clearly that the health, and, indeed, frequently 
the existence, both of mother and offspring, are secured by this physical regula- 
tion of the common parent of mankind. The human being, in reference to the 
term of existence, multiplies later, and at longer intervals, and ceases to be pro- 
lific sooner, than any other animated being with whom we are acquainted ; hence 
we find, on the average, that, in the maternal state, during its period of fruitful- 
ness, the births are not so frequent as once in 2 years. Even in the rank of 
society which is absolved from the necessity (though not from the duty) of ful- 
filling one of the most important of the maternal offices, that of feeding, from 
their own bosoms, their infant offspring, and who too often avail themselves of 
that unnatural immunity, consequently removing what our physiologists regard 
as one of the physical impediments to an accelerated prolificness,* — even in this 
rank, I find the births are at intervals of about, but rather exceeding, 2 years ; that 
period, therefore, as it respects the mass of the community, who are differently 
circumstanced in this respect, cannot be shorter. But arguments and proofs on 
this point are unnecessary, no writer having ever ventured upon supposing a 
shorter period than 2 years possible ; and even Sir William Petty, when 
labouring to prove the possibility of a doubling every 10 years for a century after 
the flood, amongst his other suppositions, so extravagant if applied to the present 
era, only lays it down, that every teeming woman can bear a child ' once in two 
years. 11 ' 

* On this subject the work of Roberton already cited may be consulted ; also a paper by 
Professor Laycock, quoted by Roberton. 



302 



DR MATTHEWS DUNCAN ON THE 



Chapter IX. — Fertility of Wives Mothers Married at Different Ages. 

Before discussing this and the next topics, it is necessary to remark that fer- 
tility may be maintained in degree in two ways — either by long-continuance or 
by intensity while it lasts. At present I omit entirely the consideration of inten- 
sity of fertility while it lasts, taking up this in the next part. But I shall show 
that, of a mass of fertile women, the younger are, on the whole, more fertile than 
the older. To demonstrate this I first adduce a Table (VII.) drawn from the data of 
St George' s-in-the-East. It is evident here that the younger women 1 1 years mar- 

TABLE VII. — Showing the Fertility op Wives Mothers Married at Differed 
Ages, from the data of St George's-in-the-East. 



Mother's Age at 
Marriage. 


11-,^ Years Married. 


21 -,'j Years Married. 


Average Number 
of Children. 


Average Number 
of Children. 


15-19 


50 


77 


20-24 


4-5 


7-0 


25-29 


4'4 ' 


6-4 


30-34 


34 


3-0 



ried, and also those 21 years married, have, on an average, larger families than the 
elder, of whatever respective ages. It must be observed that the Table includes 
all wives, who, in a small selected population, have shown any fertility. And it 
must be added that the Committee of the Statistical Society have enunciated the 
same conclusion. I quote their own words : — "The following abstract will show 
the average number of children to each marriage, at the respective periods of 10, 
20, 30, and 40 years after the birth of the first child, for each class of marriages 
formed at the four different quinquennial periods of life. 

" TABLE VIII. 



Years elapsed 

since Birth 

of First Child. 


Average number of Children to each Marriage formed at Ages 


16-20. 


21-25. 


26-30. 


31-35. 


10 
20 
30 
40 


5-05 

7-68 

8-41 

10-85 


4-51 
7-01 
7-89 
824 


4-42 
643 
6-80 
500 


3 44 
300 
7-00 
400 



LAWS OF THE FERTILITY OF WOMEN. 



303 



"It is thus obvious that marriages formed under the age of 25 are more pro- 
lific than those formed after that age, and that those formed between 16 and 20 
years of age are still more so than those at any of the superior ages."* 

As the doctrine generally taught, so far as I know, is exactly the opposite of 
that here sustained, it is important to establish the latter, if possible, by further 
proof. At another place I shall show the erroneous interpretation of the data 
which have been adduced in support of the opposite doctrine— namely, that mar- 
riages formed late in life are more prolific than those formed earlier. 

The figures now to be adduced not only confirm the doctrine that early mar- 
riages are more fruitful than late marriages ; they also explain it, showing that 
the younger married have a longer continuance of fertility than the older married, 
allowing to both the same duration of marriage, and all within the child-bearing- 
period of life. So far as the demonstration has hitherto gone, we have shown 
that the younger are more fertile than the elder ; that, excluding those who have 
no children, the younger will bear larger families than the older. We have not 
shown which bear their children most rapidly — that is, which have the greatest 
intensity of fertility while it lasts — leaving this topic for another chapter. We 
now proceed to show that, among the fertile, the younger have a longer continu- 
ance of fertility than the elder. It is this last circumstance which accounts for 
the greater fertility of the marriages of the younger. The following Table demon- 
strates this. It needs no explanation. The details are given in the footnote.f 

TABLE IX. — Showing the Amount of Continuance in Fertility of Wives 
Married at Various Ages (as shown within Twelve Months). 



Age of Mother at Marriage, .... 


15-19 


20-24 


25-29 


30-34 


35-39 


Total. 


The number Child-bearing in the 5th 1 
year of Married Life is 1 in . . .J 

The number Child-bearing in the 10th "1 
year of Married Life is 1 in . . .J 

The number Child-bearing in the 15th "1 
year of Married Life is 1 in . . . / 

The number Child-bearing in the 20th "1 
year of Married Life is 1 in . . .J 

The number Child-bearing in the 25th "4 
year of Married Life is 1 in . .J 


26 


2-7 


4-1 


4-9 


10-5 


32 


32 


4-0 


5 9 


8-7 




4 4 


4-6 


6-8 


18-2 


37-4 




80 


8-5 


14-6 


129-8 


... 




163 


680 


480 5 








171-0 



* Journal of the Statistical Society of London, vol. xi. p. 223. 

t The Table IX. may be easily seen to be made up from the following five Tables, X., XL, XII , 
XIII., Ill V. In these five Tables of the fertility of married life at different epochs, the number of 

VOL. XXIV. PART II. 4 N 



304 



DR MATTHEWS DUNCAN ON THE 



In order to derive from Table IX. more information as to the relative 
numerical value of the fertility of a mass of wives in the fifth, tenth, and fifteenth 
years of married life, and so on, I have framed the following Table (XV.) 1 
have freely pointed out the sources of error in the fundamental figures of Table 
IX. ; and after all I flatter myself that in these fundamental figures there is 
an approach to truth such as to justify the further deduction of Table XV. 

wives mothers at the respective epochs is the actual registered number in Edinburgh and Glasgow 
in 1855. The number of wives of different ages is got by estimating, and the Carlisle Table of 
Mortality is used. The estimate is not made in the exactest way, but the errors will not injure the 
comparison of the figures with one another, as the same (perhaps unavoidable) error is introduced 
into all. The results probably give a near approach to the true degrees of fertility ; for while 
among the child-bearing there are some omitted, there are probably fewer marriages omitted, and 
the numbers of wives as estimated would be too large were not a very high percentage taken off 
(1 in 100) for the special mortality of first confinements. (See Edinburgh Medical and Surgical 
Journal for October 1865, and Dr Stark's Report in the Seventh Annual Report of the Registrar- 
General for Scotland, p. xxxii.) 

To find how many women, 5, 10, and 15 years married, are alive and not widowed in 1855, 
it would strictly be necessary to have the numbers married in 1850, 1845, and 1840, from which 
the estimates should be made. Instead of doing this, I have estimated from the number married 
in 1855. As the population is increasing not greatly, this error thus introduced will not be 
great. 

It is partly with a view to correct this error that I have taken off an extravagantly high per- 
centage for the mortality of first labours. 

In making the estimate I have doubled the mortality, in order to exclude the widowed. 



TABLE X. — Fertility of Wives in the Fifth Year of Married Life. 



Ages at Child-bearing, .... 


20-24 


25-29 


30-34 


35-39 


m 

40-44 Total. | 




644 


1686 


1008 


358 


179 


3875 


Number of Wives Mothers, . 


247 


611 


244 


72 


17 


1191 


Number Child-bearing, 1 in . 


2-6 


2-7 


4-1 


4-9 


105 


3-2 



TABLE XI. — Fertility of Wives in the Tenth Year of Married Life. 



Ages at Child-bearing, 



Number of Wives, . . 
Number of Wives Mothers, 
Number Child-bearing, 1 in 



25-29 


30 34 


35-39 


40-44 


Total. 


594 


1528 


902 


313 


3337 


186 


381 


153 


36 


756 


32 


4-0 


59 


8-7 


4-4 



TABLE XII. — Fertility of Wives in the Fifteenth Year of Married Lifr. 



Ages at Child-bearing, .... 


30-34 


35-39 


40-44 


45-49 


Total. 




532 


1360 


782 


262 


2936 


Number of Wives Mothers, . . . 


116 


200 


43 


7 


366 


Number Child-bearing, 1 in . . 


4-6 


6-8 


182 


37-4 


80 



LAWS OF THE FERTILITY OF WOMEN. 



305 



only it is necessary to mention, that in this Table there are no actual values to 
keep it close to the truth. Taking, then, Table IX. as giving actual values, we 
have the fertilities for 1855 ; or for twelve months. But as 20 months has been 
shown to be the average time-unit of fertility, the fertilities of 1855 must be 
increased in like proportion ; for as 12 is to 20, so are the fertilities given in 
Table IX. to the real fertilities. All the fertile women cannot be presumed to 
have shown that quality in 12 months, but all may be presumed to have shown 
it in 20 months. In this way, the following Table (XV.) may be held as an 
estimate of the comparative amount of fertility in living children, shown by wives 
at different epochs of married life. 

The Table shows a gradually diminishing amount of perseverance in fertility 
as age advances. In illustration of the mode of reading it, I may state that 
about a half of all wives are fertile at the fifth year of married life ; more than a 
third are fertile at the tenth year of married life ; and only a fifth part of the 
whole wives arrived at the fifteenth year of married life are fertile, and so on. 

Another interesting result is got from this Table (XV.), by comparing the dif- 
ferent horizontal columns with one another. Reading the figures of adjacent 
columns obliquely from below upwards, we have a comparison of the fertility of 
a mass of wives of the same age, but of quinquennial differences of duration of 
marriage. And it is very interesting to observe that the younger married closely 
approach in fertility those married five years later in life, both being arrived at 
the same year of life at the time of the comparison. 

Short and Sussmilch maintain that early marriages are not favourable to the 
population. But, so far as I know, they adduce no satisfactory evidence what- 
ever for their belief. Yet they have considerable authority on their side, includ- 
ing the redoubtable Sadler, who arrays in his support the venerable names of 
Aristotle, of Plato, of Virgil, and of Plutarch. 



TABLE XIII. — Fertility of Wives in the Twentieth Yeae or Married Life. 



Ages at Jhild- bearing, .... 


35-39 


40-44 


45-49 


Total. 




477 


1171 


649 


2297 


Number of Wives Mothers, . 


56 


80 


5 


141 


Number Child bearing, 1 in . . 


8-5 


14-6 


1298 


16-3 



TABLE XIV. — Fertility of Wives in the Twenty- Fifth Year of Married Life. 



Ages at Child-bearing, .... 


40-44 


45-49 


Total. 


Number of Wives Mothers, . . 
Number of Child-bearing, 1 in . 


408 

6 

68-0 


961 
2 

480-5 


1396 

8 
171-0 



306 



DP MATTHEWS DUNCAN ON THE 



TABLE XV.— Showing the Probable Amount of Continuance in Fertility, 
at Different Epochs, of Wives Married at Various Ages. 



Age of Mother at Marriage, .... 


15-19 


20-24 


25-29 


30-34 


35-39 Total. 


The proportion Child-bearing about the \ 
5th year of Married Life is 1 in . . j 


1 56 
641 


1-62 
61-7 


2-46 
406 


294 
340 


6-30 
15-9 


1-92 
52-1 


The proportion Child-bearing about the ) 
10th year of Married Life is 1 in . j 


1-92 
52-1 


2-40 
41-7 


3 54 
28-2 


5-22 
192 




2 64 
37 9 


The proportion Child-bearing abont the ) 
loth year of Married Life is 1 in . .( 

or a Percentage of 


2-76 
362 


408 

245 


1092 
91 


2244 
45 




4-80 
20 8 


The proportion Child-bearing about the ) 
20th year of Married Life is about 1 in j 


5-10 
196 


8-76 
11-4 


77-88 
13 




... 


9-78 
10-2 


The proportion Child-bearing about the ) 
25th year of Married Life is about 1 in J 

or a Percentage of 


40-80 
2-4 


288-3 
•35 




... 


... 


102-6 
•97 



It is to be remarked that I only object to tliis statement of these authors so far 
as the increase of the population is concerned, and I do not consider the diminished 
chances of survival which children of very early marriages are believed to have. 
There can be, in my opinion, no doubt that early marriages are most favourable 
to the population ; and, as I have already shown that wives under 20 are less 
fecund than those from 20 on to at least 24 years of age,* the fertility of the younger 
as a mass is the more striking. But although most highly fertile as a mass, the 
iiumber of sterile among those married under 20 years of age is not inconsiderable, 
and it is probably this amount of sterility which, while satisfactory statistical 
evidence was deficient, has given rise to the error now 7 commented upon. The 
authors referred to give no definition of what they mean by early marriage. 
Whatever they may mean, they have no good evidence for their doctrine. 

Quetelet-j- enunciates on this topic the following doctrine, as a natural conse- 
quence from his data and reasonings. A marriage, says he, if it be not barren, 
produces the same number of births at whatever period it takes place, provided 
the age of the woman does not exceed 26 years. After this age the number of 
children, he adds, diminishes. Not only do I, of course, think Quetelet wrong in 

* Trans. Royal Society, 1864. f Treatise on Man, p. 15. 



LAWS OF THE FERTILITY OF WOMEN. 307 

his conclusions, but I cannot in his work discover any satisfactory grounds for 
them. 

Before passing from the perseverance in fertility of the early married, I will 
point out a difficulty of which it gives the solution. In my former paper, read to 
this Society, I showed that initial fecundity in wives from 15 to 19 years of age, 
is far less than at any age from 20 to 34 ; that is, of the young women very 
much fewer have children within two years ; at the same time, I showed that 
the fecundity of the mass of wives in our population is greatest at the commence- 
ment of the child-bearing period of life, and after that epoch gradually diminishes ; 
that is, those not the most fecund do, as a mass, produce most children. These 
two propositions are, at first sight, difficult to reconcile ; and it is accordingly 
satisfactory to be able to show that the greater continuance in fertility of the 
mass of younger wives is the explanation of the apparent anomaly. To illustrate 
how the Tables read, in affording this explanation, I may state, that while I 
formerly showed that the wives from 15 to 19 years of age are not so fecund as 
those from 20 to 24 years of age, the Tables last adduced show that at the 5th 
year of marriage, the youngest married — that is, at ages from 15 to 19 — already 
surpass all others in fertility, 1 in 26 bearing; that at the 10th year of marriage 
they still further surpass in fertility all others, 1 in 3-2 bearing ; and that at the 
15th year of marriage, they in a still higher degree surpass all others, 1 in every 
46 bearing children, within a year. 

Finally, under this head, I notice an important element of the inexactness 
that enters into the data here used, namely, the occurrence of second and third 
marriages. But the influence of this element is almost certainly inconsiderable 
for the following reasons: — In cases of second and subsequent marriages, the 
data used are exclusively those of the last marriage; as far as is known, a 
woman's previous marriage does not interfere with her subsequent fertility ; it is 
shown in this paper, that a woman's previous fertility tends to ensure continuance 
in fertility ; it will be shown that a woman's previous fertility tends to diminish 
the intensity of her subsequent fertility, when that is compared with the fertility 
of women late in being married and having family ; and the admixture of second 
and subsequent marriages in the data which include only the last marriage, 
would tend to diminish the force of the results, as bearing out these con- 
clusions. They are therefore all the more secure, from the fact of the inter- 
mingling of some data which would diminish their apparent influence. 

Another inconsiderable element of inexactness I shall only mention, the 
occurrence of twins, and both being counted in the figures. 

Chapter X. — Fertility of Persistently Fertile Wives of different Ages. 

I may here repeat that, by persistently fertile, I mean fertile up till the time 
of the collection of the data. And I adduce a Table which clearly shows, so far 

VOL. XXIV. PART II. 4 O 



J 



308 



DR MATTHEWS DUNCAN ON THE 



as the mass of figures can be relied on, that the fertility of the elder is greater 
than of the younger, while it lasts ; or, in other words, the fertility of the elder 
is the more intense. 



TABLE XVI. — Showing the Intensity - of Fertility- in Wives Mothers of 

Different Ages.* 





Mother's Age. 


Duration of Marriage. 




15-19. 


20-24. 


25-29. 


30-34. 


35-39. 


40-44. 


45-49. 


Under 5 years, . 


1-128 


1-519 


1-825 


1-844 


1-827 


1-698 


1-200 


5 years and under 10, 


2-500 


3-190 


3-750 


4048 


4085 


3-792 


4000 


10 years and under 15, 


... 


5333 


5-453 


5-903 


6197 


5964 


6-500 


15 years and under 20, 




... 


6-000' 


7-379 


7-914 


7-993 


8-435 


20 years and under 25, 




... 


... 


7000 


9-396 


9-718 


10-528 


25 years and under 30, 


... 








... 


12-368 


13-600 




... 




... 




... 


... 


13000 



The conclusion here arrived at is founded upon lengths of married life. Were 
the figures such as to give, instead of lengths of married life, lengths of intervals 
between the births of first and last children, the results would be still more 
striking ; for I have already shown that in the case of the elder, fertility is later in 
beginning to show itself than in the younger. 

If, as I have shown, the younger are more prolific than the elder, and if, as 
also I have shown, the elder are more intensely fertile, while their fertility lasts, 
than the younger in the same time ; then, it necessarily follows, as a corollary, 
that the fertile women married younger have a longer continued fertility than 
the fertile women married older. In no other way can the younger surpass the 

* The following Tables give all the details and calculations from which Table XVI. is 
constructed : — 

TABLE XVII.— Or Women under 5 Years Married. 







No. of 
Mothers. 


No. of 
Children. 


Average to 
each Mother. 




7,183 


11,880 


1-654 


Mother's age — 16 to 19 years, . 

20 to 24 „ . 

25 to 29 „ . 

30 to 34 „ 
,, 35 to 39 „ 
„ 40 to 44 „ 

45 to 49 „ 




374 

3,180 

2,460 

833 

277 

53 

5 


422 

4,829 

4,489 

1,536 

506 

90 

6 


1128 
1-519 
1-825 
1-844 
1-827 
1-698 
1200 



LAWS OF THE FERTILITY OF WOMEN. 



309 



elder in their whole fertility; a conclusion which has already been otherwise 
demonstrated. 

It may also be here pointed out, that the figures of Table VI. make it 
probable that elderly women when fertile, are more intensely so than younger, 
when their fertility has already resulted in a large family, for that Table shows 
that the children in large families are born very quickly one after another. 

In his work on " the Law of Population," Mr Sadler enters upon this subject 
of the varying fertility of women according to age. Seeking arguments where- 
with to overturn the teaching of Malthus, whose principles he hated as well as 



TABLE XVIII. — Of Women 5 Years Married and less than 10. 







No. of 


No. of 


Average to 






Mothers. 


Children. 


each Mother. 


4,637 


17,690 


3-815 


Mother's age- 


—16 to 19 years, . 


2 


5 


2-500 


» 


20 to 24 „ 






499 


1,592 


3-190 


)> 


25 to 29 „ 






2,155 


8,082 


3-750 


)> 


30 to 34 „ 






1,418 


5,740 


4-048 


>> 


35 to 39 „ 






461 


1,883 


4-085 


>> 


40 to 44 „ 






96 


364 


3-792 


,> 


45 to 49 „ 






5 


20 


4000 



TABLE XIX. — Or Women 10 Years Married and less than 15. 





No. of 
Mothers. 


No. of 
Children. 


Average to 
each Mother. 


2,739 


16,233 


5-930 


Mother's age — 20 to 24 years, . . 

,, 25 to 29 „ 

„ 30 to 34 „ 

„ 35 to 39 „ 

40 to 44 „ 

45 to 49 „ 


9 

415 

1,345 

814 

140 

16 


48 

2,263 

7,939 

5,044 

835 

104 


5-333 
5453 
5-903 
6197 
5-964 
6-500 



TABLE XX. — Of Women 15 Years Married and less than 20. 





No. of 
Mothers. 


No. of 
Children. 


Average to 
each Mother. 


1,280 


10,013 


7823 


Mother's age- 


-25 to 29 years, . . 


7 


42 


6-000 


,, 


30 to 34 ,, 


253 


1,867 


7379 


»> 


35 to 39 „ 


721 


5,706 


7914 


a 


40 to 44 „ 


273 


2,182 


7-993 


>> 


45 to 49 „ 


23 


194 


8-435 



310 



DR MATTHEWS DUNCAN ON THE 



opposed, he found data which at first sight appear to support his doctrine " that 
marriages are more prolific the longer they are deferred." Were this true 
doctrine, it would certainly go far to overturn the Malthusian system, and Mr 
Sadler might be justly proud of the demonstration. The facts which he adduces 
may, without cavil, be allowed to be, as he says, indisputable. It is his illogical 
use of the facts which has to be pointed out. Without pretending to enter on 
the defence of Malthusian notions, we accept Mr Sadler's challenge " to evade 
the demonstration," which the aforesaid facts afford. And it is of importance to 
do so, because, down to the latest authors, Sadler's facts and supposed demonstra- 
tions are generally quoted with unsuspicious approval.* 

The first data afforded by Sadler are derived from the records of Dr Gran- 
ville's experience as physician to the Benevolent Lying-in-Institution and the 
Westminster Dispensary, the calculations having been made by Mr Finlayson. 



TABLE XXI. — Or Women 20 Years Married and less than 25. 





No. of 
Mothers. 


No. of 
Children. 


Average to 

each Mother. 


432 


4,181 


9 678 


Mother's age- 


-30 to 34 years, . . 


1 


7 


7000 


j» 


35 to 39 „ 


134 


1,259 


9396 


>> 


40 to 44 „ 


259 


2,517 


9-718 


j> 


45 to 49 „ 


36 


379 


10528 



TABLE XXII. — Of Women 25 Years Married and less than 30. 





No. of 
Mothers. 


No. of 
Children. 


Average to 
each Mother. 


29 


371 


12-793 


Mother's age — 40 to 44 years, . . 
45 to 49 „ 


19 
10 


235 
136 


12-368 
13600 



TABLE XXIII.— Of Women 30 Years Married. 





No. of 
Mothers. 


No. of 
Children. 


Average to 
each Mother. 


1 


13 


13000 


Mother's age — 45 to 49 years, . 


1 


13 


13000 



See Boudin, Traite de Geographie et de Statistique Medicales, &c, tome ii. p. 59. 



LAWS OF THE FERTILITY OF WOMEN. 



311 



TABLE XXIV. — Showing the Effect the Postponement of the Marriages 
of Females has upon their Annual Puolificness. (Sadler.) 



Ages when Married. 


Average number of 

Births for each year 

of Marriage. 


Ages when Married. 


Average number of 

Births for each year 

of Marriage. 


From 13 to 16, . . 


•456706 


From 29 to 32, . . 


•589811 


„ 16 to 20, . . 


•503610 


„ 33 to 36, . . 


•776866 


„ 21 to 24, . . 


•520227 


„ 37 to 39, . . 


1-125000 


„ 25 to 28, . . 


•545163 







Now this Table is made from the data of lying-in charities. It is therefore 
not a Table of fertile women, but of persistently fertile women ; for every woman 
was entered in the records only when she came to have attendance in her con- 
finement. All that the Table offers is corroboration of the law enunciated in 
this chapter, that elderly women are more fertile than younger, so long as their 
fertility endures. 

It is almost incredible that so acute a reasoner, as Mr Sadler is, could be so 
deceived by appearances, as to suppose his figures showed that marriages at 39 
years of age are as fruitful as marriages of any inferior age, down to 13. Yet, 
for aught he says, he appears so to believe. 

Sadler did, indeed, get the length of seeing that the Table just given was 
somewhat deficient. " It may," he says,* " perhaps be objected to the whole of 
the foregoing proofs, that they are derived from a register which cannot profess 
to give the whole number of children which the marriages it records shall pro- 
duce, from their commencement to their termination, but only those which have 
been born to each up to a period within these limits, all the facts which it can 
record being necessarily retrospective ones. I shall, therefore," he continues, 
" proceed to another series of proofs of the same principle, which will at once 
silence every such exception, and afford a strong additional demonstration of its 
truth. These are derived from the registers of the peerage, which, as I have 
observed elsewhere, I have gone through in order to collect a body of authentic 
facts illustrative of many of the principles advanced in these volumes. As far as 
they relate to the subject before us, those facts are as follows :"— 

* Law of Population, vol. ii p. 279. 



VOL. XXIV. PART II. 



4p 



312 



DR MATTHEWS DUNCAN ON THE 



TABLE XXV. — Showing the Effect of the Postponement of the Marriages 
of the Peeresses on their Prolificness. (Sadler.) 



Period of Marriage. 


Number 
of Marriages. 


Number 
of Children. 


Births to each 
Marriage. 


From 12 to 15, . . . 
„ 16 to 19, . . . 
„ 20 to 23, . . . 

„ 24 to 27, . . . 


32 
172 
198 

86 


141 

797 

1033 

467 


440 
4-63 
521 
5-43 



To this Table of Sadler's many objections may be made, such as the paucity 
and insecurity of the data, as also their deficiency, the highest age of marriage 
included in them being only 27, and all notice of the important element of the 
duration of marriage being omitted. 

Sadler not only erred in supposing he had demonstrated that late marriages 
are more prolific than early. He was ignorant also that a larger proportion of 
the elder than of the younger wives bears no children at all, and that an elderly 
Avoman continues fertile a shorter time than a younger, counting, in both cases, 
only up to periods within the child-bearing portion of life. 

It is a natural, and I believe a true, notion, that twin-bearing should be a 
sign of intense fertility in woman, as the number of a litter certainly is in 
bitches, and other inferior animals. In confirmation of this notion, and of the 
law of intensity of fertility now demonstrated, we find that women are more likely 
to bear twins the older they are. This subject is capable of some interesting 
developments ; but, as I have already elsewhere* entered upon them, I shall add 
no more in this place, merely remarking, that they were completed at a time 
when the law of intensity of fertility was only guessed at, and, therefore, Avhen 
the explanation of the great twin-bearing of old women was not known to me. 

In like manner, it is natural to suppose that the length and weight of children 
should go with intensity of fertility. But my researehesf seem to show that this 
is not the case, but that length and weight of children go with the intensity of 
fecundity, or likelihood of bearing children, according to age. Professor PTecker, 
of Munich, has, however, elaborately shown that my conclusions on this head do 
not agree with those derived from his larger data.t Mine are based on 2087 
observations only, and I am willing, in the meantime, to hold it as subjudice. 
whether his or my conclusions are to be received. His do appear to me the more 

* Edinburgh Medical Journal for March and April 1865. f Ibid., December 1864. 

i Monatsschrift fur Geburtskunde und Fiauenkranklieiten, November 1865. 



LAWS OF THE FERTILITY OF WOMEN. 313 

probable, because they bring the laws of length and weight of children, according 
to the mother's age, into agreement with the law of intensity of fertility here 
demonstrated. 

Chapter XI. — The Fertility of Elderly Women. 

So ardently did Sadler desire the triumph of his attack on Malthus, that he 
adopted the dream of Mason Good, who says, " that the usual term (of cessation 
of the menses) is between 40 and 50, except where women marry late in life, in 
which case, from the postponement of the generative orgasm, they will occasion- 
ally breed beyond their fiftieth year" ! ! * Mason Good refers to some extraordi- 
nary cases of pregnancy in old women, curiosities in physiology, but he adduces 
no good evidence in favour of the doctrine he here propounds. An opposite doc- 
trine is taught by Burns, an author equally celebrated, and much more worthy 
of confidence in a question of the kind now before us " It is well known," says 
the Glasgow Professor,! " that women can only bear children until a certain age, 
after which the uterus is no longer capable of performing the action of gestation, 
or of performing it properly. Now it is observable, that this incapability or im- 
perfection takes place sooner in those who are advanced in life before they marry, 
than in those who have married and began to bear children earlier. Thus we 
find, that a woman who marries at forty shall be very apt to miscarry, whereas 
had she married at thirty, she might have born children when older than forty ; 
from which it may be inferred, that the organs of generation lose their power of 
acting properly sooner, if not employed, than in the connubial state. The same 
cause which tends to induce abortion at a certain age, in those who have re- 
mained until that time single, will also, at a period somewhat later, induce it in 
those who have been younger married ; for in them we find that, after bearing 
several children, it is not uncommon to conclude with an abortion ; or sometimes 
after this incomplete action, the uterus, in a considerable time, recruits, as it 
were, and the woman carries a child to the full time, after which she ceases to 
conceive." My own opinion has always coincided with that so well expressed 
by Burns ; and I may add, that the curious observations regarding abortion at 
the close of the fertile period of life has its analogue in the lower animals. Several 
times I have been told by men of experience, that an old bitch often ends her 
career of breeding by a dead and premature pup. Whitehead also J regards 
those pregnancies which occur near the termination of the fruitful period in women 
as being among the most commonly unsuccessful. 

In Edinburgh and Glasgow in 1855, 53 women above the age of 45 bore living 

* The Study of Medicine. 1822. Vol. iv. p. 63. 
f Principles of Midwifery. Tenth Edition, p. 309. 
\ On Abortion and Sterility, p. 247. 



314 THE FERTILITY OF WOMEN. 

children. Among these 53, only one was primiparous — her age was 49, and she 
had only been one year married ; 2 bore second children, — 1 was aged 46 years, 
and had been four years married — the other was aged 52 years, and had been 
three years married ; 4 bore fourth children ; 4 bore fifth children ; 3 bore sixth 
children ; 3 bore seventh children ; 6 bore eighth children ; 8 bore ninth children ; 
7 bore tenth children ; 4 bore eleventh children ; 1 bore a twelfth child ; 4 bore 
thirteenth children ; 2 bore fourteenth children ; 1 bore a fifteenth child ; 2 bore 
sixteenth children; 1 bore a nineteenth child. In short, the great majority 
of women child-bearing late in life are mothers of considerable families, not 
women for whom a postponement of the generative orgasm has to be imagined, 
a circumstance which destroys all shadow of ground for Mason Good's supposi- 
tion. * 

This completes my remarks on the fertility of married women. But the 
subject is susceptible of further interesting developments, by an inverted method 
of proceeding, which I hope to carry out. 

It is evident that the conclusions arrived at in this paper, or others still more 
definite, can alone form a sure basis for speculation in the great questions in 
political economy regarding population, and the various means of increasing it, 
or of retarding its excessive growth. And it is to be hoped that the promoters of 
that science will avail themselves of information which Malthus, Sadler, and 
their followers, evidently desired ardently to possess. In default of this infor- 
mation, they have fallen into many manifest errors in their groping after truth. 

But it is not to the political economist alone that such information is valuable. 
It will form an element in the guidance of social life, and will certainly greatly 
contribute to the wisdom in council of the well-informed medical practitioner. 

* For other corroborative evidence, see Roberton, Physiology and Diseases of Women, p. 184. 



( 315 ) 



XXIII— On some Laws of the Sterility of Women. By J. Matthews Duncan, M.D. 

(Read 19th February 1866.) 

Before commencing the discussion of the subject, it is necessary to make some 
definitions, with a view to avoiding the confusion which extensively prevails, 
from the neglect of the all-important definition of terms. I might be even more 
exact than I shall be, and excuse myself from adopting such a seeming improve- 
ment, on the ground that further refinement of definition would itself cause con- 
fusion in the present stage of advancement of our knowledge. 

Absolute sterility, I shall hold to mean the condition of a woman who, under 
ordinary favourable cirumstances for breeding, produces no living or dead child, 
nor any kind of abortion. 

Ste?*ility, I shall hold to mean the condition of a woman who, under ordinary 
favourable circumstances for breeding, adds not even one to the population, or 
produces no living and viable child. 

Relative sterility, I shall hold to mean the condition of a woman who, while 
she may or may not be absolutely sterile, while she may or may not be sterile, 
is, under ordinary favourable circumstances for breeding, sterile in relation to 
the circumstance of time ; or, in other words, in relation to her age, and the dura- 
tion of her married life. 



Chapter I. — Sterility of Marriages in our Population. 

Under this head, the age at marriage, and the duration of it, are not regarded. 
We simply compare the number of people living in the married state, without 
and with living children. The only information I have on this point is derived 
from the writings of Dr Stark.* " It is a pity," says he, " that when the census 
was taken up, a query had not been put to every married woman, whether she 
had borne children. We have at present no means of ascertaining what propor- 
tion of the marriages proves unfruitful ; and it is no criterion to ascertain the 
number of married persons who had children living with them on the night of 
the census. Married persons who had a numerous family, may have none with 
them, because they are grown up, or are absent at schools or trades. We know, 
however, from other sources, that a considerable proportion of marriages proves 
unfruitful ; and as it was shown that the married women of Scotland produce 

* Census of Scotland, 1861. Population Tables and Report, vol. ii. p. xxxvi. 
VOL. XXIV. PART II. 4 Q 



316 DR MATTHEWS DUNCAN ON SOME 

more children in proportion to their number, than the married women of England, 
it would have been extremely interesting to have ascertained whether that 
depended on more of the Scottish married women being fruitful." 

On this point I may here interpolate the observation, that, in my opinion, it 
is highly improbable that there is any essential difference in the fecundity of 
women in England and in Scotland. The researches now published make it 
necessary, with a view to settling the question raised by Dr Stark, to look into 
the comparative ages at marriage of the women in England and Scotland ; a 
difference in that respect alone may prove sufficient to afford the solution of the 
whole matter. And like remarks are applicable to the supposed great fertility of 
Irish women. 

" As it may," continues Dr Stark, " however, give a distant approximation, 
it may be stated, that taking two of the largest registration districts of Glasgow, 
it was found, that of 14,523 married persons living together, 11,718 had children 
living with them ; while 2805 had no children with them. This would yield the 
proportion of 80-686 per cent, with children, and 19*314 per cent, without 
children ; or, without the decimals, that in every 100 married couples, 81 had 
children, while 19 had none. These numbers may be safely taken as the propor- 
tion in the town populations, seeing that for each district the proportions came 
out within a very small decimal fraction of one another; also from the circum- 
stance, that in other tables which have been published in the Registrar-General's 
second detailed Annual Report, relative to the proportions of children born by 
mothers at different ages in Edinburgh and in Glasgow, the results of the one 
town almost exactly corresponded with those of the other.'" 



Chapter II. — Sterility of Wives. 

The wives who do not increase the population, may be called sterile. But a 
wife who has one or several abortions, or who bears one or several dead children, 
or to whom both of these events happen, adds not a unit to the population ; yet 
such a wife cannot be said to be absolutely sterile. In order to discover the 
amount of sterility of married women, I proceed on the following plan. I take 
the registers of Edinburgh and Glasgow for 1855, and find what is the number of 
first children produced in that year. With this I compare the number of mar- 
riages in that year. It is evident that the first children only should be counted, 
for they indicate all the wives who are not sterile. If one living child is born to 
a marriage, that marriage is not sterile. Further, it is evident that, although 
the first births in 1855 will not all pertain to the women married in that year, it 
may be assumed that, if the marriages be nearly the same in number for a few 
contiguous years, the first births in one year will give the fertility very accurately 



LAWS OF THE STERILITY OF WOMEN. 317 

of any of the contiguous years. From this fertility, the sterility can be easily 
computed. 

Now, in 1855, there were, in Edinburgh and Glasgow, 4447 marriages, and 
3722 first deliveries of living children, leaving 725 marriges sterile, or 1 in 61. 
But in these figures are included 75 marriages which did not take place till after 
the women had passed 44 years of age, and these will damage the physiological 
value of the statement, as these 75 women could not be expected to be prolific. 

Of women between the ages of 15 and 44 inclusive, there were married 4372 ; 
among wives of the same ages, 3710 had first children, leaving 654 marriages 
sterile, or 1 in 66. In other words, 15 per cent, of all the marriages between 15 
and 44 years of age, as they occur in our population, are sterile. 

The statement of the amount of sterility just given appears to me, from the 
largeness of the figures used, to be far more valuable than any other I know of. 
But on account of their great interest, I shall quote the statements of two authors.* 
" In the Dictionnaire des Sciences Medicales (vol. vi. p. 245 ; see also Neue Ab- 
handlungen der Schwedischen Akademie der Wissenschaften, vol. xi. p. 70), it is 
stated," says Sir James Y. Simpson,! "that Hedin, a Swedish minister, had noticed 
that in his parish, composed of 800 souls, one barren woman is not met with for 
ten fertile. It is further stated, that Frank asserted, but from what data is not 
mentioned, that it would be found on investigation, that in most communities 
containing 300 to 400 couples, at least 6 or 7 would be sterile, without anything 
in their physical condition to explain the fact. It seems to have been from this 
assertion of Frank's, that Burdach, who is almost the only author who even 
alludes to the matter, has given the general statement, that one marriage only in 
50 is unproductive (Dr Allen Thomson's excellent essay on Generation, in Todd's 
Cyclopaedia, vol ii. p. 478, foot note). 

" For the purpose of ascertaining the point by numerical data, I had a census 
taken of two villages of considerable size, viz., Grangemouth in Stirlingshire, and 
Bathgate in West Lothian, — the one consisting principally of a seafaring popula- 
tion, and the other of persons engaged in agriculture and manufacture. 

" The following form the results in these two places: — Of 210 marriages in 
Grangemouth, 182 had offspring ; 27 had none ; or about one marriage in 10 was 
without issue. Of the 27 unproductive marriages, all the subjects had lived in 
wedlock upwards of five years, and in all, the female had been married that 
period before she reached the age of 45. Again, of 402 marriages in Bathgate, 
365 had offspring; 37 had none; or about one marriage in 11 was unproductive. 
There were at the same time living in the village 122 relicts of marriages, and of 

* Lever's statement I here quote, but I cannot ascribe much value to it, because no evidence 
is adduced, and because there is an evident numerical error in some part of the passage. He says. 
" It is found that ^th, or 5 per cent, of married women are wholly unprolific." — Organic Diseases 
of Uterus, p. 5. 

| Obstetric Works, vol. i. p. 323. 



L 



318 DR MATTHEWS DUNCAN ON SOME 

these 102 were mothers; 20 were not mothers; or about 1 in 6 had no family. 
In all, of 467 wives and widows, 410 had offspring ; 57 had none ; or about one 
marriage in 8 was unproductive. Of these last 57, six had not been 5 years 
married, and there were other six above the age of 45 when married. If we sub- 
tract these 12, we have, of 455 marriages, 410 productive; 45 unproductive; or 
1 in 10?jth without issue. 

"Returns such as I have just now adduced are exceedingly difficult to 
obtain, in consequence of no registers being anywhere kept, so far as I know, that 
could be brought to bear upon the question. If it had been otherwise, I would here, 
if possible, have gladly appealed to a larger body of statistical facts, in order to 
arrive at a more certain and determinate average of the proportion of unpro- 
ductive marriages in the general community. For the purpose, however, of 
extending this basis of data, I have analysed, with some care and trouble, the 
history of 503 marriages, detailed by Sharpe, in his work on the ' British Peer- 
age,' for 1833. Among British peers, there were 401 marriages with issue ; 102 
without issue ; or of 503 existing marriages among British peers in 1833, 74 
were without issue, after a period of five years. Of those who had not yet lived 
in the married state for five years, 28 were still without family ; and in Burke's 
' Peerage,' for 1842, there still remained among these 28 marriages, 7 without 
issue, making 81 as the total number of unproductive marriages among the 
original 503 ; or the proportion of the unproductive to the productive marriages 
among this number is, as nearly as possible, 1 in 6f . In the above calculation, 
I have excluded 8 unproductive marriages, in which the age of the husband at 
the date of marriage exceeded 56. These 8, however, ought to be deducted from 
the original sum of total marriages that were included ; or, in other words, the 
503 should be reduced to 495, and then the whole result would stand thus :— 
among 495 marriages in the British Peerage, 81 were unproductive, or 1 in (j| 
were without any family." The proportion of unproductive marriages in Grange- 
mouth, Bathgate, and the British Peerage, all taken together, was found by 
Simpson to be 1 in8-f-. 

Dr West* states, that he found the general average of sterile marriages, 
among his patients at St Bartholomew's Hospital, to be 1 sterile marriage in 
every 8*5.f 

Chapter III. — Absolute Sterility of Wives. 

In order to arrive at the absolute sterility of the wives in Edinburgh and 
Glasgow, it is necessary to add to the number of wives bearing first living children, 
the number of those who bear only dead children or abortions. 

* Diseases of Women, 3d edition, p. 3. 

f A statement of the sterility of Esquimaux women is given by Roberton, Essays and Notes 
on the Physiology and Diseases of Women, p. 53. 






LAWS OF THE STERILITY OF WOMEN. 



319 



The number of abortions has been variously estimated by Graunt, Short, 
Whitehead, and others. The number of children born dead has been the subject 
of much investigation, among others by Jacquemier, Boudin, and Legoyt. But 
were our information on these points very exact, it would not help us in this 
inquiry. For our purpose, the desideratum is not the number of abortions in 
a number of pregnancies, nor the number of children born dead in a number of 
births, but the proportional number of married women who produce nought else 
than abortions or dead children ; who, while not absolutely sterile, yet add none 
to the population. Of this class of wives I know of no estimate.* I believe they 
are few, and I leave the statement of the sterile as a near approximation to a 
correct statement of the absolutely sterile. 

Chapter IV. — Sterility according to the Ages of Wives. 

To illustrate the variations of sterility according to age, I bring forward the 
accompanying Table (I.). 



TABLE I. — Showing the Variations of Sterility according to the Ages 

of the Wives. 



Ages of Wives at Mar- "l 
riage, .... J 


15-19 


20-24 25-29 

1 
i 


30-34 


35-39 


40-44 


45-49 


50, &c. 


Total. 


Number of Wives, . 
First Children, . . . 
Sterile Wives, 
Percentage Sterile, . 


700 

649 

51 

7-3 


1835 
1905 




1120 
809 
311 

27-7 


402 
251 
151 
37-5 


205 

96 

109 

53-2 


110 

10 

100 

90-9 


46 

2 

44 

95-6 


29 

29 
100 


4447 

3722 

725 

16-3 


Proportion Sterile, 1 in 


13-72 





3-60 


2-66 


1-88 


1-10 


1-05 


1-00 


6-13 



With the numbers of marriages taking place in Edinburgh and Glasgow in 
1855, at different ages of the wives, are compared the numbers of first children 
born in the same year to wives married at the same ages in that year or pre- 
viously. The number of sterile wives is got by subtracting the latter figures from 
the former, and the percentage of sterile marriages is given in the penultimate 
horizontal line. 

So far as the numbers are to be relied upon, we have from this Table the in- 
teresting results, that about 7 per cent, of all the marriages between 15 and 19 
years of age inclusive, and as they occur in our population, are without offspring ; 
that those married at ages from 20 to 24 inclusive, are almost all fertile ; and 

* The following extract from the work of Dr West, on Diseases of Women (3d edit., p. 367), 
may be of some value. It refers to the histories of a set of poor women labouring under uterine 
cancer. " There were but two out of the whole 150 women, whose pregnancy had issued merely in 
abortion." 

VOL. XXIV. PART II. 4 R 



320 



DR MATTHEWS DUNCAN ON SOME 



that, after that age, sterility gradually increases according to the greater age at 
the time of marriage. 

Chapter V. — Expectation of Sterility. 

The main element in the expectation of sterility is the age of the woman at 
marriage. This has just been described. But, besides this, our statistics suggest 
to us other laws as to the expectation of sterility. Of these the first is : — 

That the probability of a woman 's being sterile is decided in 3 years of married 
life. For while a large number are fertile in each of the first three years of 
married life, only 7 per cent, of the fertile bear after 3 years of marriage, or about 
1 in 13. 

TABLE II. — Showing the Fertility of Mothers, of different Ages at Marriage, 

COMMENCING AFTER THREE YEARS OF MARRIED LlFE. 



Mother's Age at Marriage, . 


15-19 


20-24 


25-29 


30-34 


35-39 


40-44 


45-49 


Total. ! 


Number of Fertile, 


649 


1905 


809 


251 


96 


10 


2 


3722 


Number commencing Fertility 1 
after being 3 years married, J 


63 


119 


62 


27 


15 


1 




287 


Percentage commencing Fer- \ 
tility after being 3 years > 


9-7 


6-2 


7-7 


10-7 


15-6 


10-0 


... 


7-7 




10-3 


160 


13-0 


9-3 


6-4 


100 


... 


13-0 



This same Table affords us a second law of expectation of sterility : — 
That when the expectation of fertility is greatest, the probability of sterility is 
soonest decided, and vice versa. For our Tables show that of the wives married 
from 20 to 24 who are all fertile, only 6 2 per cent, begin to breed after three 
years of marriage ; while at the other ages, with less fecundity, a greater per- 
centage commences after the completion of the third year of marriage. 

Chapter VI. — Relative Sterility. 

Here I take into consideration only those who have borne children, only those 
who are not sterile. Of course all these wives, if they survive in wedlock, will 
sooner or later become relatively sterile. Now, in a paper lately read to this 
Society, I showed that the prolongation of fertility was greater according as the 
age at marriage was less. From this conclusion it is easy to derive one in regard 
to relative sterility, to the effect that : — 

Relative sterility will soone? arrive according as the age at marriage is greater 






LAWS OF THE STERILITY OF WOMEN. 



321 



The demonstration of these proportions is arrived at by showing the proportional 
numbers bearing at different years of married life, according to age at marriage. 
This is an indirect way of proceeding, but it is the only one I can find available, 
while I have no documents giving the ages of mothers at marriage, and their ages 
at birth of last children, the mothers continuing to live in wedlock. 

TABLE III. — Showing the relative Sterility op a mass of Wives Married at 

DIFFERENT AGES AT SUCCEEDING EPOCHS IN MARRIED LlFE. 





15-19 


20-24 


25-29 


30-34 


35-39 


Total. 


Proportion Sterile about the 5th Year of Married | 


2-78 
35-9 


2-61 
38-3 


1-68 
59-4 


1-51 
66-0 


1-19 
84-1 


209 

479 


Proportion Sterile about the 
Married Life is about 1 in . 
or a percentage of . 


10th Year 


*} 


2-09 
47-9 


1-71 
58-3 


1-39 
71-8 


1-24 
80-8 




161 

62-1 


Proportion Sterile about the 
Married Life is about 1 in . 
or a percentage of . 


1 5th Year 


of| 


1-57 
63-8 


1-32 
75-5 


1-10 
90-9 


1 05 
95-5 




1-26 

79-2 


Proportion Sterile about the 
Married Life is about 1 in . 
or a percentage of ... . 


20th Year 


- } 


1-24 
80-4 


113 
88-6 


101 

98-7 






111 
89-8 


Proportion Sterile about the 
Married Life is about 1 in . 


25th Year 


° f } 


102 
97-6 


100 
99-65 


... 






101 
99 03 



Table III. gives the calculated amounts of sterility at different periods of 
married life in women married at different ages. It is needless to enter on the 
method of construction of this Table. It is merely the complement of Table XV., 
given in my former paper, where full details are stated. I shall only state, that 
this Table is all calculated for 20 months, with a view to giving the nearest 
accurate estimate, 20 months being what I have called the time-unit of fertility, 
the shortest time within which all women may be expected to show fertility if 
they possess it. 



Chapter VII.— Expectation of Relative Sterility. 

As a sort of appendix to this paper, I produce five Tables, giving all the 
details of the expectation of continued fertility ; and conversely, of relative 
sterility. These Tables not only give data for calculating the chances of relative 
sterility, but also for calculating the probable number of the family produced in 
women at different ages becoming relatively sterile. To enter further upon these 



322 



DR MATTHEWS DUNCAN ON SOME 



considerations would be merely to give in writing what is more succinctly stated 
in the Tables themselves. 

TABLE IV. — Fifth Year op Married Life. 





1st 


2d 


3rd 


4th 


5th 


6 th 


7th 


8th 


9th 


Total. 


Wives Mothers, of Ages 20-24, . 
Proportion of above to 644 Wives 1 
Married at from 15-19 is 1 in J 


13 
49-5 


39 
16-5 


160 
4-0 


31 
20-8 


4 
161-0 


... 


• • 


•• 




... 


247 
2-6 

611 
2-7 


Wives Mothers, of Ages 25-29, . 
Proportion of above to 1686 Wives "1 
Married at from 20-24 is 1 in J 


10 
168-6 


82 
20-5 


398 
4-2 


106 
15-9 


13 2 

13-0 '843-0 


... 


•• 






Wives Mothers, of Ages 30-34, . 
Proportion of above to 1008 Wives 1 
Married at from 25-29 is 1 in J 


3 
336-0 


31 
32-5 


147 
6-8 


52 
194 


8 
126-0 


2 
5040 


1 
1008 


•• 




... 


244 
4-1 


Wives Mothers, of Ages 35-39, . 
Proportion of above to 358 Wives "I 
Married at from 30-34 is 1 in J 


3 
119-3 


12 
29-8 


37 

9-7 


14 
25-6 


1 
358- 


1 
358- 


2 
179- 


1 
358- 


1 
358- 


72 
4-9 


Wives Mothers, of Ages 40-44, . 
Proportion of above to 179 Wives "I 
Married at from 35-39 is 1 in J 


3 
59-6 


2 
89-5 


11 

16-3 


1 
179- 








... 


... 


17 
10-5 


Total Wives Mothers, of Ages 20-44, 

Proportion of above to 3875 Wives 1 

Married at from 15-39 is 1 in J 


32 
121-1 


166 
23-3 


753 
51 


204 
19-0 


26 
149- 


5 

775- 


3 
1291-6 


1 
3875- 


1 
3875- 


1191 
3-2 



Lastly, I state a law of relative sterility for which I do not here adduce the 
numerical proofs, these having already been given in my paper lately read to the 
Society. This law is, that :— 

A wife who having had children has ceased for three years to exhibit fertility, 
has probably become relatively sterile ; that is, will probably bear no more children ; 
and the probability increases as time elapses. For the probability of sterility only 
commences after three years of sterile marriage. Further, the data given in 
Table II. of the paper just referred to, show that fertile women bear a child, on 
an average, about every two years, so long as they remain fecund. The data 
given in Table VI. show that successive children in a family succeed one another 
with an average interval of about 20 months. To these propositions I have to 
add the general consent, shown in the same paper, that fertile wives breed 
generally every two years ; consequently, that no class breeds, though indi- 
viduals do, at shorter intervals ; and no class breeds at longer intervals, though 
individuals do so. Considering these different statements, it is apparent to 
the student, that there is no room left for any but a very inconsiderable number 
of women to breed at longer intervals than two years. For were there any con- 



LAWS OFTHE STERILITY OF WOMEN. 



323 



siderable number of wives breeding at longer intervals, the averages just given 
would be far overpassed. And some of these averages are, as already shown, 
considerably less than were believed to be the true averages by writers who were 
not thinking of the law now demonstrated, but of the ordinary rate of time- 
fertility of married women. 

Besides, being of evident intrinsic value, the conclusions arrived at in this 
paper will afford to medical men, means of estimating the utility of the many 
vaunted methods of curing sterility which are now much in vogue, and which, 
considering the nature of the condition to be cured, justly excite anxiety for the 
honour of the profession in the minds of its best friends. 

TABLE V. — Tenth Year of Married Life. 



Number of Child, 


1st 


2d 


3d 


4th 


5th 


6th 


7th 


8th 


9th 


10th 


11th 


Total. 


Wives Mothers, of "1 
Ages 25-29, . j 

Proportion of above to ^ 
594 Wives Married > 
at from 1 5-19 is 1 in J 


... 


1 

594- 


14 
42-4 


30 
19-8 


78 
76 


51 
11-6 


8 

74-2 


4 
148-5 


3 

509-3 


... 




186 
3-2 

381 
40 


Wives Mothers, of 1 
Ages 30-34, . ) 

Proportion of above to \ 
1528 Wives Married V- 
atfrom 20-24 is lin j 


1 

1528- 


4 
382- 


17 
89-9 


55 
27-8 


148 
10-3 


105 
14-5 


34 
44-9 


11 
1389 


1 
1528- 


2 
764- 


Wives Mothers, of "1 
Ages 35-39, . ] 

Proportion of above to ^ 
902 Wives Married V 
atfrom 25-29 is 1 in J 




2 
451- 


4 

225-5 


19 
47-5 


60 
15- 


48 
18-8 


13 
69-4 


5 
180-4 


2 
451- 


... 




153 

5-9 


Wives Mothers, of "1 
Ages 40-44, . J 

Proportion of above to j 
313 Wives Married I 
atfrom 30-34 is lin J 


... 




5 

626 


11 
285 


10 
31-3 


6 
52-2 


2 
156-5 

57 
58-5 


1 
313- 

21 
158-9 


5 

6674 


1 
313- 




36 
8-7 


Total Wives Mothers, 1 
of Ages 25-44, . ( 

Proportion of above to ^ 
3337WivesMarried V 
atfrom 15-34islin J 


1 
3337- 


7 
476-7 


40 
83-4 


115 
29-0 


296 
113 


210 
15-9 


2 
16685 


2 
1668-5 


756 
44 



VOL. XXIV. PART II. 



4 S 



324 



DR MATTHEWS DUNCAN ON SOME 
TABLE VI. — Fifteenth Year of Married Life. 





Number of Child, . . 


1st 

1 

532- 


2d 


3d 


4th 


5th 


6th 


7th 


8th 


9th 


10th 


llth 


12th 


13th 


Total 




"Wives Mothers, of ) 
Ages 30-34, . . 1 

Proportion of above to ^ 
532 Wives Married >■ 
at from 15-19 is 1 in ) 


3 
1773 


2 
266- 


6 

88-7 


11 

48-4 


18 
29-6 


24 
22-2 


28 
19-0 


18 
29-6 


2 

266- 


1 

532- 


1 
532- 


1 

532- 


116 
46 




Wives Mothers, of ) 
Ages 35-39, . . f 

Proportion of above to 1 
1360 Wives Married [■ 
at from 20-24 is 1 in J 






5 
272- 


4 
340- 


18 
75-5 


32 
42-5 


53 
25-6 


41 
33-2 


29 
46-9 


14 
97-1 


2 

680- 


1 
1360- 


1 

1360- 


200 

6-8 

43 
18-2 




Wives Mothers, of \ 
Ages 40-44, . . j 

Proportion of above to ^ 
782 Wives Married I 
at from 25-29 is 1 in ) 






1 

782- 


2 
391- 


4 
195-5 


7 
111-7 


12 
65-2 


14 
55-9 


2 
391- 


1 

782- 




... 


... 




Wives Mothers, of \ 
Ages 45-49, . . j 

Proportion of above to ^ 
262 Wives Married > 
at from 30-34 is 1 in j 








1 

262- 


1 
262- 


l 
262- 


... 


1 

262- 


2 
131- 




1 

262- 




... 


7 
37-4 




Total Wives Mothers, ) 
of Ages 30-49, . . j 

Proportion of above to ^ 
2936 Wives Married V 
at from 15-34 is 1 in J 


1 
2936- 


3 

978-6 


8 
367- 


13 
225-8 


34 
86-3 


58 
50-6 


89 
33-0 


84 
34-9 


51 
57-5 


17 
172-7 


4 
734- 


2 

1468- 


2 

1468- 


366 
8-0 



TABLE VII. — Twentieth Year of Married Life. 



Number of Child, . . 


4th 


5th 


6th 


7th 


8th 


9th 


10th 


llth 


12th 


13th 


Total. 


Wives Mothers, of Ages 1 
35-39, . . . . j 

Proportion of above to } 
477 Wives Married > 
at from 15-19 is 1 in ) 




... 


2 

2385 


5 
95-4 


5 
95-4 


17 

280 


15 

31-8 


9 
53- 


3 
159- 


... 


56 
8-5 


Wives Mothers, of Ages) 
40-44, . . . . ) 

Proportion of above to^ 
1171 Wives Married > 
at from 20-24 is 1 in j 


1 

1171- 


1 

1171- 


2 

585-5 


9 

130- 


14 
836 


28 
41-8 


8 
1464 


13 
901 


2 

585-5 


2 

585-5 


80 
14-6 


Wives Mothers, of Ages) 
45-49, . . . . j 

Proportion of above to^ 
649 Wives Married > 
at from 25-29 is 1 in ) 






... 






3 
216-3 




1 
649 


1 

649 


... 


5 

129-8 


Total Wives Mothers, 1 
of Ages 35-49, . j 

Proportion of above to") 
2297 Wives Married [• 
at from 15-29 is 1 in ) 


l 

2297- 


l 

2297- 


4 
574-2 


14 
164- 


19 
121- 


48 
47-8 


23 
999 


23 
99-9 


6 

383- 


2 

1148- 


141 
16-3 



LAWS OF THE STERILITY OF WOMEN. 



325 



TABLE VIII. — Twenty-Fifth Year op Married Life. 



No. of Child, 


10th 


11th 


12th 


13th 


14th 


15th 


16th 


17th 


Total. 


Wives Mothers, of Ages 40-44, 
Proportion of above to 408 \ 
Wives Married at from 15-19, J 


2 

204- 


2 

204- 


1 

408- 


1 

408- 








... 


6 

68- 


Wives Mothers, of Ages 45-49, 
Proportion of above to 961 } 
Wives Married at from 20-24, J 




1 

961- 


... 


... 








1 

961- 


2 

480-5 


Total Wives Mothers, of Ages 1 
40-49, J 

Proportion of above to 1369 1 
Wives Married at from 15-24, J 


2 

684- 


3 

456- 


1 

1369- 


1 
1369- 








1 

1369- 


8 
171- 



( 327 ) 



XXIV.— On a New Property of the Retina. By Sir David Beewster, K.H., 

D.C.L., F.R.S., &c. 

(Read 19th February 1866.) 

In a paper on Hemiopsy, published in the present volume of the Transactions 
(p. 15), I have mentioned the remarkable fact, that the parts of the retina which 
are insensible to visual, are sensible to luminous impressions, the light being 
occasioned by irradiation from the adjacent parts of the retina. The parts thus 
affected in hemiopsy extend irregularly from the foramen centrale to the margin 
of the retina ; but the space which they occupy is so small, their distribution so 
irregular, and the time of their continuance so short, that it is difficult to make 
such observations upon them as would establish a general property of the 
retina. 

Mr Airy, our distinguished Astronomer-Royal, who has had more than 
twenty attacks of hemiopsy, has been induced, by the perusal of my paper, to 
describe their character, and delineate the form of the parts 
insensible to visual impressions.* The hemiopsy, in his 
case, commences at the foramen centrale c, Fig. 1, and ex- 
tends outwards in a zig-zag curve line, the curve "being 
small at first, and gradually increasing in dimensions,''' as 
shown in the figure. It is accompanied with "tremor 
and boiling so oppressive, that if produced only in one 
eye, they may nearly extinguish the corresponding vision 
in the other," and it lasts from twenty to thirty minutes. IriTT 

It occurs sometimes on one side, and sometimes on the 
other side, of the foramen ; and Mr Airy has " never been able to decide with 
certainty whether the disease really affects both eyes." On one occasion, when 
under its influence, he lost " his usual command of speech, and his memory failed 
so much that he did not know what he had said, or had attempted to say, and 
that he might be talking incoherently." He, therefore, entertained "no doubt 
that the seat of the disease was in the brain ; that the disease is a species of 
paralysis; and that the ocular affection is only a secondary symptom." 

From these important facts, it will be seen that Mr Airy's case differs essen- 
tially from mine, in which the locality of the indistinctness occurs in irregular 

* Philosophical Magazine, July 1865, vol. xxx. p. 19. 
VOL. XXIV. PART II. 4 T 





32& SIR DAVID BREWSTER ON A 

zig-zag lines proceeding, as in Fig. 2, from the foramen outwards, and not in a 

circular arch, as shown in Fig 1. The " general obscuration," mentioned by 

Mr Aiky, shows that the luminous impression on the 

affected parts is not so strong in his case as in mine, and 

that the retina is still sensible to light derived from the 

surrounding parts by irradiation. The severity of the 

affection in Mr Airy's case is remarkable. In mine the 

attack is little more than disagreeable, and I have never 

experienced the slightest effect either upon the speech 

or the memory. I have given this brief abstract of Mr 

Amy's interesting paper from the relation of hemiopsy 

to the permanent affection of the retina which I am 

about to describe. 

When without the hope of obtaining any precise information respecting the 
irradiation into the parts of the retina affected with hemiopsy, an accidental 
observation revealed to me the disagreeable fact that a considerable portion of 
the retina of my right eye was absolutely blind, or insensible to visual impres- 
sions ; and I have thus been enabled, from the extent and permanence of the 
affection, to make whatever observations were necessary to ascertain the true 
character of the phenomenon. 

The portion of the retina thus affected with what may be called local 
amaurosis is situated, in the field of vision, about 15° from the foramen, in a line 
to the left inclined 45° to the horizon. Its angular magnitude is about G° in its 
greatest breadth, which corresponds to a space about the twenty-eighth of an 
inch on the retina. 

When the image of a bright object covers the whole, or any part of this spot, 
it is invisible. If the image is the flame of a candle, or of the moon, or of the 
sun near the horizon, it is wholly invisible. The eye is therefore at this part of 
it absolutely insensible to light falling upon it from without. If we now direct 
the eye to the sky, to the white ceiling of a room, or to any extended white sur- 
face, no dark spot, even of the slightest shade, is seen in the field of vision. The 
portion of the retina, therefore, insensible to light incident upon it directly, or 
from without, has been illuminated by irradiation from the surrounding parts. 
But for this wise provision, an eye affected with local amaurosis would carry 
about with it a black spot, disfiguring the aspects of nature, and ever reminding 
the patient of his misfortune. 

How long this condition of my retina has existed, I cannot discover. It may 
have existed for half a century, or more ; and, but for a casual observation, its 
existence might never have been discovered. Whether it came on gradually, or 
was produced in some of the experiments in which the eye was exposed to the 
light of the sun, I have no means of ascertaining. If from the first of these 



NEW PROPERTY OF THE RETINA. 329 

causes, it is likely to extend itself; if from the second, it may remain as it is. 
Having observed it only for a year without noticing any enlargement, it is 
probable that it was produced by the strong action of light. 

Owing to the compound structure of the retina, consisting of different layers, 
and these layers composed of bodies of different shapes, it is very difficult to dis- 
cover the part which each of them performs in the act of vision ; but considering 
each element of the retina as a rod, the end of which next the vitreous humour 
is an expansion of the optic nerve, we know that distinct vision of external 
objects arises from the law of visible direction, by which every ray of light, at 
whatever angle it may fall, gives us vision of the point from which it proceeds, 
in a direction perpendicular to the part of the membrane on which it is incident. 
When this outer layer of the retina is insensible to the light of external objects, 
its luminosity, or the light which it exhibits, may be received from the surround- 
ing parts of the expanded nerve by irradiation, or from the parts of the elemental 
rods behind it, if they were not paralysed, or if they are, by the action of the un- 
paralysed rods around them. 

Although in hemiopsy, and in the case of local amaurosis which I have 
described, the paralysed parts are still luminous, yet there are cases in which these 
parts are absolutely black, and into which no light is introduced by irradiation. 
An example of this fact presented itself to me in the 
morning of the 16th October 1837, and is represented in 
Fig. 3, where two black curved lines proceeded from the 
foramen centrale of the retina of the right eye. These 
lines were so black that, in the memorandum which I 
made at the time, I state that they were blacker than 
the black ink lines upon the paper. The lines continued 
only about ten minutes, and were probably produced by 
the pressure of blood-vessels, as I had, the day before, ^mTz 

been subject to much giddiness. In this case, the elemen- 
tary rods of the retina beneath these lines must have been paralysed throughout 
their length ; and, therefore, it is probable that in the cases of hemiopsy and 
local amaurosis, the paralysis affects only the end of the rods in contact with 
the vitreous humour, and formed by the expansion of the optic nerve. 

In concluding this notice, T would suggest to philosophers and medical prac- 
titioners the importance of studying the manner in which sight and hearing 
are, in their own case, gradually impaired, for it is in the decay or decomposition 
of organic structures, as well as in their origin and growth, that valuable 
results may be presented to the physiologist ; and facts of this kind have a 
peculiar value when the patient is himself a practised observer. 




( 331 ) 



XXV. — On the Classification of Chemical Substances, by means of Generic 
Radicals. By Alexander Crum Brown, M.D., D.Sc. 

(Read 5th February 1866.) 

The idea of chemical structure, as founded on that of atomicity (or the equiva- 
lence of atoms), enables us to divide any molecule, whose chemical structure is 
known, into radicals. The number of ways in which this may be done increases 
with the complexity of the molecule. Each of these modes of division corre- 
sponds to a series of conceivable reactions, some of which have been observed. 
Any one of these series may be made the basis of classification ; but it is obviously 
most convenient to select for this purpose the most characteristic reactions, and 
those which are common to such substances as form natural groups. In studying 
these, we find that each series implies the presence of a particular radical, 
within which the reactions in question take place. We may call such series of 
reactions the Generic reactions, and the corresponding radicals Generic radicals. 
These are sometimes residues of double decomposition, but very frequently this 
is not the case, and this may account for the fact, that the importance of these 
generic radicals has been very much overlooked. 

I shall consider some of the cases in which this principle of classification is 
already, to some extent, recognised, before proceeding to apply it generally, and 
examine first those examples furnished by groups of bodies which are referred to 
the types H 2 and NH 3 . 

I. A large number of the substances referred to the type H 2 0, are formed by 
the replacement of one atom of H in each molecule of H 2 0, by a radical, as, — 



\0 C 2 H 5l C 2 H 3°1 A) So}°&c 



V}0, H 2 )0, 

The part common to all such bodies is the radical (HO) 7 or jj j- 0, and the reactions 

common to the group affect this radical alone. These reactions are — 1st, The 
replacement of (HO)'; 2d, The replacement of H in (HO/; and 3d, The 
replacement of in (HO)'. Thus (HO) may be replaced by CI, Br, &c, or (HO), 
by ; (HO)' may become (KO)', (C 2 H 5 0)', &c. by the replacement of H, or (HS) , 
(HSOJ', &c. by replacement of 0. (HO)' is therefore the generic radical of this 
large genus. 

II. An extensive series of substances referrible to the type NH 3 have only 
, one atom of H in each molecule of ammonia replaced. 

VOL. XXIV. PART II. 4 u 



332 DR A. CRUM BROWN ON THE CLASSIFICATION OF 

As «£.}, , CAO| Nj a H,O,| Ni JjJH = : }N, fc 

•"■2 ) -"-2 J ' 

In these we have (NH 2 )', or jj j- N common to the group. The generic reactions 

are — 1st, Replacement of one or both atoms of H in NH 2 by radicals. 2d, The 
addition of two monatomic atoms to each NH 2 , N'" becoming N v . 3d, The replace- 
ment of N"' by 0" and (HO)' (by the action of nitrous acid), or what comes to the 
same thing, the replacement of NH 2 by HO. All these affect the radical NH 2 alone, 
which is therefore the generic radical. In the same way (NH)" is the generic 
radical of the substances derived from ammonia, by the replacement of two 
atoms of H. 

The best way of extending this method of classification generally, is to examine 
the chemical structure of those bodies which form well-marked genera, and see 
what group of atoms they have in common, and whether the common group (or 
radical) is that part of the molecule, in which the reactions characteristic of the 
genus take place. One very well-marked genus is that of the monobasic acids, 
which have aldehydes and alcohols corresponding to them (Kolbe's " Monocar- 
bonsauren"). As examples, we may take acetic acid, acrylic acid, benzoic acid, 
and cinnamic acid. The chemical structure of these substances is represented, as 
far as known, by the following graphic formulae : — 

® ^ (")(») («)<■) 

©-0-0-0 ©-©-0-9=© 0_0_0=© ©-<Q)-©-(^)=0 
© © © © © ri'X© AAXKfi 

X X © © y uu @©y 

^^ ^^ (0 (in 

Acetic Acid. Acrylic Acid. Benzoic Acid. Ciunamic Acid. 

-0=0 

The part common to all these acids is obviously the monatomic radical 

(h) 

and the generic reactions take place within it ; the salts are formed by the 
replacement of the H by metal, — chlorides, bromides, aldehydes, &c, by the 
replacement of the (HO)', by CI, Br, H, &c. ; alcohols from the aldehydes, by the 

-©:© <? 

addition of H 2 X becoming -©-©-© ; amides, by the replacement of (HO)' 

© 
by NH 2 ; nitriles, by the replacement of 0"and (HO)' by N"'; acetones, from two 
molecules, by the loss of CO(HO) in one, and the substitution of the radical 
thus produced for HO in the other. {(CO(HO)}' is, then, the generic radical of 
these acids. As this radical is of very great importance, it is advisible to indi- 



CHEMICAL SUBSTANCES BY MEANS OF GENERIC RADICALS. 333 

cate it by a single symbol, and I shall use the Greek letter H for this purpose.* 
The relation of 5 to CN, or of the acid to the nitrile, is seen not only in the mono- 
basic acids (monocarbonsauren), but also in the di- and tri-basic acids (di- and tri- 
carbonsauren), so that these contain the radical 3, two and three times respectively. 
The investigation sketched above also shows that COH and CH 2 (HO), are 
the radicals of the aldehydes and the "true" alcohols. Pursuing this method 
further, we arrive at a system of classification for the various groups of pseudo- 
alcohols, the number of which has recently increased so much. One of these 
groups is formed by the hydrogenation of the acetones. The acetones have the 
general- formula COR 2 (in which R 2 may represent either two atoms of the same 

0-0=0 
or of two different radicals) ; taking the graphic formula, we have Y 



(-©-© being the generic radical), by the addition of H 2 , we get Y the 

0-0-0 

© 
reaction being similar to that by which the aldehydes are converted into true alco- 
hols, one of the two pairs of equivalents by which the atom is united to the C, 
being separated, and hydrogen added to each of the equivalents (one of and one of 
C), thus rendered free. The generic radical here is obviously {(CTI(HO)} ", and the 
subgenera and individual substances are determined by the radicals saturating 
the two free equivalents of this generic radical. This genus, besides the universal 
character of the alcohol family (the formation of ethers) has the property of form- 
ing aldehydic bodies (acetones) by the loss of two atoms of H, {CH(HO)}" be- 
coming (CO)"; and in that subgenus which contains the radical {CH 2 (HO)} / (or 
in which one of the R's is H), this aldehydic body is a true aldehyde, capable of 
forming an acid by further oxidation. When none of the equivalents of the carbon 
atom in the generic radical are directly saturated with H, the alcohol is incapable 
of producing an aldehyde or acetone; and, in this case, we have the characteristic 
radical reduced to {C(HO)} /// , as in Butlerow's trimethyl alcohol. We thus see 
that the most generalform of alcohol is C(HO)R 3 (where R 3 represents one triatomic, 
or one diatomic and one monatomic, or three monatomic radicals) ; and the genera, 
sub-genera, and individuals of this family are determined by the nature of the 
radical or radicals, combined with the family radical {C(HO)| /// . For con- 
venience let us, in the meantime, represent this radical by the symbol 3>'". 
The different subdivisions of the family will then be R'"$, R'lt^, and R' 3 $ If 

* I had proposed to express the radical (COHO)' by the symbol H, before I was aware that 
Butlerow had already used the symbol A to represent the same radical. While fully acknowledging 
the priority of Butlerow's recognition of this radical, I prefer to retain the symbol H. Bv using 
such of the Greek capitals as differ from the Roman in form, to represent generic radicals, we avoid 
the danger of confounding them with elementary atoms. 



334 



DR A. CRUM BROWN ON THE CLASSIFICATION OF 



-* 



the original and ingenious speculations of Kekule on the constitution of the 
aromatic bodies should be experimentally confirmed, phenylic alcohol would be 
an example of the first form (C 5 H 5 )'"$.* The second and third form may be sub- 
divided into genera, having the generic radicals (R'&)". As we have seen, by far 
the most important of these is that containing Ho, and it maybe convenient to ex- 
press this by a separate symbol, say ". Under this genus we have two forms, R"0 
and R' 2 0. The so-called ketones of the dibasic carbon acids (dicarbonsiiuren) may 
be regarded as the aldehydes of unknown alcohols of the first form ; thus succinone 

© 




© 



may be considered as the aldehyde of the 
unknown alcohol, ..... 






©0 

To the second form R' 2 0, belong the greater number of known alcohols, and 
a considerable number of bodies possessing alcoholic properties, though not 
generally classified with the alcohols. They form aldehydes or acetones by oxi- 
dation ; and this reaction is not confined to those substances to which the 
name alcohol is commonly applied : for instance, mesoxalic acid is the aldehyde 
(or acetone) of tartronic acid, alloxan that of dialuric acid, gryoxylic acid 
that of gly collie acid. Confining our attention to those substances of the form 
R/ 2 e, in which R is of the form {CJI 2n+1 )', and has its C atoms arranged in 

the simplest way (-0-0-0-, &c), we may form the following series of 

sub-generic radicals H©, CH 3 0, C 2 H 5 ©, &c. The first of these we have seen to be 
the radical of the " true" alcohols, and it seems probable that the second is that 
of the hydrates of the defines. The arguments in favour of this view (which 
undoubtedly requires and admits of further experimental research) may be 
stated thus : — The first member of the series, the hydrate of ethylene, is identical 



with common alcohol, and has the formula ^^i 



n ifu 




The 



* Translating Kekule's graphic formula for phenylic alcohol into the system used in this 



paper, we have 




in which we have the triatomic radical C(HO) united to the tria- 



tomic radical C 5 H 5 . 



f Using the symbol ( ho )— as a contraction for (h)_(o)— . 



CHEMICAL SUBSTANCES BY MEANS OF GENERIC RADICALS. 



335 



hydrate of propylene is almost certainly identical with the alcohol derived from 

© 



acetone, which is 





CH 
or qtt 3 [ 0. The constitution of hydrate 



of butylene has not been directly ascertained, but as it is obviously metameric with 

butylic alcohol, and as it is in the highest degree improbable that its C atoms are 

CH ) 
arranged in a different way, we may safely assume that its formula is „ tt [ 0, 






In all these bodies we have the radical _©. 

© 
| 0, and from the similarity of the method by which the others are pro- 
duced, it is reasonable to infer that they are similarly constituted. If so, while 
the " true" alcohols have the water residue united to what we may call a 
terminal C atom, the olefine hydrates have the water residue united, not to this, 
but to the C atom next to it. As both alcohols give the olefine by dehydration, 
the carbon equivalents deprived of HO and H, must be those which are combined 
with HO, the one in the one, and the other in the other. Thus : — 



0-(p-©-®-H 2 O = ©-©-©-®, and ©-(jD-©-®-H 2 = ©-®-©-©, 
©© © © © © 

Olefine Hydrate. 



True Alcohol. 



Olefine. 



Olefine. 



So that 




-©-© (C 2 H 3 )' must be the generic radical of the olefines. As the 

© 

true alcohols are formed from the aldehydes, or, as they may be called, the formo- 

ketones (as produced by distilling a mixture of formiate of lime with another lime 

CH ) 
salt), so we may presume that the alcohols -n 3 [ ®, may be produced from the 

aceto-ketones (the ketones formed by distilling acetate of lime with other lime 
salts), and the same is no doubt the case with all the other genera of pseudo- 
alcohols of the form R' 2 0. (HCO)', (CH 3 CO)', (C 2 H 5 CO)', &c, becoming (H©'), 
(CH 3 ©)', (C 2 H 5 ©)', &c. The same considerations would, of course, apply to other 
series besides that of completely saturated bodies, but it is unnecessary to do more 
than mention this as Linnemann's benzhydrol (C 6 H 5 ) 2 stands, as yet, alone as a 
pseudo-alcohol of this class among non-saturated bodies. 

VOL. XXIV. PART II. 4 X 




336 DR A. CRUM BROWN ON THE CLASSIFICATION OF 

Derived from the aldehydes and acetones, we have another series of substances, 
having well-marked reactions in common, and forming what we may call a 
subgenus of the genus containing the radical H. These are the acids obtained 
by the action of HC1 and HCN, on the aldehydes and acetones. The mode of 
formation of these acids appears to be the following : — To the aldehyde or ketone 
HCN is first added in the same way as H 2 is added to form the alcohol, a body 
which may be called an oxynitrile being then produced. 

© 
© 

© ° © 

(this stage of the reaction can be traced in the case of bitter almond-oil ; the so- 
called hydrocyanate of bitter almond-oil being, no doubt, the nitrile of mandelic 
acid). In the second stage of the reaction this nitrile is decomposed (like other 



nitriles) by the HC1 and water, yielding NH 4 C1, and the acid ©-©-©-© 

©© 



by this reaction it will be seen that the radical (CO)" has been transformed into 
(C(HO)H)" or ($H)", which is therefore the generic radical of this series of acids. 
This genus may (like the acetones) be subdivided still further, the aldehydes 
giving rise to acids containing ($HE)' (or 0H), the acetoketones to those containing 
(0CH3S)', &c. The best known of these subdivisions is that containing (05)'. 
As indicated by the generic radical, these bodies have the properties both of acids 
and alcohols, giving rise to salts by the replacement of the hydrogen in the 5 by 
metals, and to ethers by the replacement of the (HO) in the by salt radicals 
(acids minus H). Some of them, at least, seem capable of forming aldehydes ; for, 
as Debus has pointed out, glyoxylic acid is the aldehyde of glycollic acid. (It is 
worthy of note, that glycollic acid is the only member of the series which is a 
" true" alcohol, containing the radical (H0)', and giving rise, by oxidation, to an 
aldehyde and an acid — glyoxylic and oxalic acids). The typical formulas of Fkank- 
land and Duppa indicate in a different way the same constitution as that 

[OP 

HO 

expressed by the radical formulae above ; C 2 , ttt) being obviously identical with 

R 2 



CHEMICAL SUBSTANCES BY MEANS OF GENERIC RADICALS. 337 

© © 

© © 

©-©-©I© and if we write oxalic acid (S) 2 , thus ©Z©-©Z© it is plain that 

(£> © 

© © 

the acids of the lactic acid series may be derived from it by replacing 0" by R 2 . 

Kolbe long ago suggested, and Maxwell Simpson has since proved, that 
the dibasic and tribasic carbon acids are related to two and three molecules 
respective of carbonic acid, in the same way as the monobasic acids are to one 
molecule of the same substance. They therefore contain the radical H two and 
three times respectively. Similarly, we might expect to find bodies containing 
the derived radicals (COH*), (CH 2 HO), &c, two or three times, forming thus 
diatomic and triatomic aldehydes, alcohols, &c. We only know one diatomic 
aldehyde, glyoxal (COH) 2 , and with certainty, only one diatomic true alcohol, 
glycol (CH 2 HO) 2 . From the way in which the other glycols are formed, it will 
be seen, that if the view of the structure of the olefines suggested above be correct, 



HO ) 



1U i 1 n.Kj I 

they contain the radical V^ (cV/h) (formed by replacing Br by HO in 

© 




which again is formed by the direct addition of Br 2 , to © ©~©), and it is 

© © 
only when this radical is united to H that the glycol can be a true alcohol on 

both sides. Taking this view, propylenic glycol is a compound of the radicals 
(H©)', and (CH 8 ©)' ; amylenic glycol of (H©)' and (C 3 H 7 0y, and so of the others, 
one of the atoms of water residue being in the position of the HO in a true alcohol, 
the other in that of an olefine-hydrate. Of course, it is quite conceivable, and 
indeed very likely, that there are bodies which contain the radical (CH 2 HO) 
twice or oftner, and are thus polyatomic true alcohols ; but, with the exception of 
ethylenic glycol, they are as yet unknown. In treating of diatomic alcohols, we 
cannot pass over the curious body obtained by Wurtz, by the addition of water to 
allyl. A consideration of the chemical relations of acrylic acid, acrolein and 
allylic alcohol to propionic acid, propionic aldehyde and propylic alcohol indicates 



f °\Sormu?a h01 ©"©-C^-©-© and for allyl 0-©-©- 
© © © © © 



©-©' 
i i 

© © 



©-©-© 
(5) © 



It is therefore a diatomic olefine, containing the radical (C a H a y twice, and if its 



338 DR A. CRUM BROWN ON THE CLASSIFICATION OF 

reactions correspond to those of the monatomic olefines the formulae of Wuetz's, 
dihydriodate and dihydrate will be, — 

®@®®©® ®0[®® 

®-©-®-©-©-©-©-® and @ _©_ ( i > ' 
® ® @® ® @ X ^ 



-©-©- 
i i 

ft) fa 



-©-©-® 
i i 

® ® 



the latter will thus contain the radical (CH 3 e)' twice, and be a diatomic olefine- 
hydrate. 

The organic acids derived from sulphuric acid, and which are formed by the 
addition of S0 3 to organic substances containing hydrogen, stand in the same rela- 
tion to sulphuric acid as the carbon acids (carbonsauren) do to carbonic acid ; in 
these we have an organic radical replacing one HO in S0 2 (HO) 2 . They there- 
fore contain the radical S0 2 (HO) ; which, assuming the hexatomic character of 
the sulphur atom in sulphuric acid, may be represented by the graphic formula, 

fsj As we have numerous generic radicals derived from {(CO) HO}' 

®-®^ ' 

such as COH, CH 2 (HO), we might expect to find similar derived radicals 
from S0 2 (HO), and there can be little doubt that substances containing such 
radicals exist ; but as yet very few of them are known. Thus we have only 
one or two substances corresponding to the acetones, such as sulpho-benzid, 
(C 6 H 5 ) 2 S0 2 ; a few chlorides containing S0 2 C1, but no bodies corresponding to 
the aldehydes or alcohols.f The remarkable substance discovered by V. Oefele, 
and named by him " Trisethyl sulphin oxydhydrat," and which has the formula 
S i7 (C 2 H 5 ) 3 (HO), is a proof of the possibility of such bodies. This substance has 
the same relation to sulphurous acid that Butleeow's trimethyl alcohol has to 
carbonic acid. 

As the radical COHO unites with itself to form oxalic acid, so we have 

®hr® 
S0 2 HO, forming hyposulphuric acid (S0 2 HO) 2 fsj 

®-®^ ^" 



®^r® 



( - 



0-0. 

The examples of generic radicals might be considerably increased in number, 
but as the purpose of this paper is not so much to tabulate known substances, 
as to show how this may be done, those given above may suffice. It will be 
seen that by this method, bodies having strongly marked chemical reactions in 
common are placed together. The relations between different genera are 

* As this radical occurs very frequently, it may be advantageous to have a single symbol for 
it, and I have been in the habit of using the Greek letter 2 for this purpose. Thus we have CH 3 S, 
acetic acid ; CH 3 2 methylsulphuric acid ; CH 2 S2 sulphacetic acid, &c. 

f See Kolbk, Lehrbuch der Organischen Chemie, Bd. ii. s. 742. 



CHEMICAL SUBSTANCES BY MEANS OF GENERIC RADICALS. 339 

prominently brought forward, and the vacancies, not yet filled np by experi- 
ment, in the list of conceivable compounds, distinctly pointed out. 

The division of molecules into two parts, one more readily undergoing chemical 
change than the other, presents certain analogies to the " Theory of Copulae," 
proposed by Berzeltus. This is most marked in the case of the acids con- 
taining (COHO)', and (S0 2 HO)'. On the theory of copulse, these acids contain 
oxalic acid C 2 3 , H 2 0, or hyposulphuric acid S 2 5 , H 2 0, and a copula. Thus 
acetic acid was considered as C 2 H 6 , C 2 3 , H 2 0, sulpho-benzolic acid as C 12 H 10 , 
S 2 5 , H 2 0, &c. ; according to the view which is taken in this paper, acetic acid 
contains the- h alf of C 2 H 6 (methyl), and the half of oxalic acid ; sulpho-benzolic 
acid, the half of C 12 H 10 (phenyl), and the half of hyposulphuric acid. In the 
same way, the older chemists regarded hydrochloric acid as H 2 C1 2 , a com- 
pound of the molecule H 2 , with the molecule Cl 2 , while we now consider it as con- 
taining the halves of these molecules. It is therefore as correct to say, that acetic 
acid is a compound of methyl and oxalic acid, as that hydrochloric acid is a 
compound of hydrogen and chlorine. To prevent confusion, it is however better, 
whenever it can be done, to have separate names for the radical and the substance. 
Thus we may call (COHO)' Carboxyl (as proposed by Bayer), and distinguish 
it from (COHO) 2 oxalic acid, (S0 2 HO) / might be called Sulphoxyl, and thus be 
distinguished from (S0 2 HO) 2 hyposulphuric acid. Even in the case of those 
radicals whose names are the same as the isomeric substances, we may, in some 
instances, make the distinction ; thus (CH 3 )' is methyl, (CH 3 ) 2 methyl gas, (CN)' 
cyanogen, (CN) 2 cyanogen gas, CI' chlorine, Cl 2 chlorine gas. 

In conclusion, it may be interesting to enumerate some of those substances 
which consist entirely of generic radicals — all of whose reactions are therefore 
generic reactions — thus we have cyanogen gas (CN) 2 , consisting of two atoms of 
the generic radical of the nitriles united together ; glyoxal (COH) 2 ; glycol 
(CH 2 HO) „ or (©H) 2 ; oxalic acid (COHO) 2 , or H 2 ; hyposulphuric acid (S0 2 HO) 2 , or 
2 2 , ; tartaric acid (probably) (CH(HO)) a (COHO) 2 , or (93), ; glycolic acid (CH 2 H0) 
(COHO), or (®H)S; glyoxylic acid (COH) (COHO), or (COH)E; tartronic acid 
CH(HO) (COHO) 2 , or©H 2 ; glycerine (probably) (CH 2 HO) 2 (CH(HO)), or® (©H) 2 ; 
glyceric acid (CH 2 HO) (CH(HO)) (COHO), or (©H) {39) ; mesoxalic acid (CO) 
(COHO) 2 , or COH 2 . 



VOL. XXIV. PART II. 4 Y 



( 341 ) 



XXVI. — Some Observations on Incubation. By John Davy, M.D., F.R.S., 

Lond. and Edin. 

(Read April 16, 1866.) 

The observations which I have now the honour to submit to the Society were 
made chiefly with the intent to endeavour to ascertain whether, in the instance 
of the egg of the common fowl, that which may be presumed to be vital action 
can for a while be arrested, and yet be capable of renewal. Whilst this was the 
main object kept in view in conducting the trials, a secondary one was to observe, 
however cursorily, the changes which take place in the contents of the egg when 
vital development has been prevented. 

Of the many experiments I have made, during a period of more than two years 
that my attention has been directed to the inquiry, I shall select those, the results 
of which were best defined, or were least ambiguous. Considering the obscurity of 
the subject, it seems best to give the particulars of each of the selected trials, 
though, in so doing, I have to fear that the details may prove tedious. 

In all the trials, newly or recently laid eggs were put under the hen for in- 
cubation, with those which were the special subject of experiment. 

I. Of Unimpregnated Eggs. 

The trial with these was made as a preparatory measure in relation to those 
which were to follow. 

Four eggs were selected, obtained from a hen that had been kept apart after 
her last sitting. Of these, three in their fresh state were put under a hen with 
eleven ordinary eggs ; the fourth was left exposed to the air in a room, the tem- 
perature of which varied from about 60° to 65° Fahr. on the 15th June, the day 
they were placed for incubation. 

No. I weighed 727'5 grs. l No. 3 weighed 801*6 grs. 
2 ... 8515 „ 4 ... 8434 „ 

On the 9th of July the eleven impregnated eggs were hatched, producing healthy 
chickens. The three unimpregnated were found to be little altered. Again 
weighed, the loss of each, per cent., was as follows : — 



No. 1, . 


14-6 grs. 


No. 3, . 


.. 12-3 grs. 


2, . 


.. 13-7 „ 


4, . 


.. 2-7 „ 



The three from under the hen sank in water. Each broken under water, yielded 

VOL. XXIV. PART II. 4 Z 



342 dr john davy's 

a little air ; that from No. 1 was found to consist of 20 of oxygen, 80 of azote ; 
that from No. 2 was of like composition. In neither could any carbonic acid be 
detected by milk of lime. 

The appearance and qualities of the contents of both these eggs were similar. 
The white and yolk were distinctly apart, each confined in its proper membrane. 
There was no unpleasant smell from either. The white was quite transparent, 
with a slight yellowish tinge ; the yolks were of their natural colour, with here 
and there spots of a lighter colour on their surface. The chalazse were readily 
detached. Neither white nor yolk, when triturated with hydrate of lime, gave off 
the slighest ammoniacal odour, nor showed more than a faint fume when brought 
near a rod dipped in hydrochloric acid, a fume but little stronger than when water 
was substituted. Under the microscope, the appearance of the yolk differed but 
little from that of the yolk of an ordinary egg fresh and impregnated. 

The egg No. 3 was not now examined ; it was kept exposed to the air, with 
No. 4. These, on the 16th of October, were found, on weighing, to have sustained 
an additional loss — No. 3 of 96 per cent., No. 4 of 8-7 ; and on the 23d of Nov- 
ember, when again weighed, of a further loss — No. 3 of 2-5 per cent., No 4 of 34. 

Broken under water, No. 3 gave off a good deal of air of an offensive smell, 
that of sulphuretted hydrogen predominating. A portion collected was found to 
consist of 15 per cent., absorbable by milk of lime, chiefly carbonic acid, and of 
85 not diminished by phosphorus, chiefly, if not entirely, azote. The contents of 
this egg were much changed : there was no distinct yolk or white, but a semifluid 
mixture of a whitish milky hue, partly curdled, with which were intermixed 
gelatiniform greenish masses, which, under the microscope, appeared to consist 
of cells and granules, the former suggestive of a kind of mucedo. 

No. 4, broken under water, yielded a good deal of air, which had no odour, and 
which, on examination, was found to consist of about 20 per cent, oxygen and 80 
azote, without any appreciable quantity of carbonic acid. The contents of the egg 
were hardly perceptibly altered ; as of Nos. 1 and 2 the white and yolk were 
distinct, each in its proper membrane ; the white showed an alkaline reaction ; 
the yolk neither an acid nor alkaline ; mixed with hydrate of lime, neither af- 
forded a perceptible smell of ammonia. 

A second trial with unimpregnated eggs, conducted in the same manner as 
the preceding, was made with some from a Bantam hen that had been kept 
secluded. Five of her eggs a few days old (the oldest ten days) were put under 
a hen on the 21st November, with two ordinary eggs, which in due time were 
hatched, producing healthy chickens. On examination, after twenty-one days, 
two of the Bantam eggs were found broken. The remaining three were undergoing 
putrefaction; their contents were very offensive, a fluid, of a greenish hue, contain- 
ing scattered through it small masses of a dark green colour, almost black. Under 
the microscope, its lighter portion exhibited granules and oil globules, its darker 



OBSERVATIONS ON INCUBATION. 343 

matter that of a hyaloid transparent substance without cells. The fluid was 
coagulated by heat. The air collected from one of them consisted of 40 per cent, 
carbonic acid, 2 oxygen, 58 azote. 

No contrast could be greater than the appearance and state of the unimpreg- 
nated eggs in these two trials ; in the first, with the exception of No. 3, so little 
changed, in the last so much changed, so much so as to be suggestive of the death 
of the eggs, the formation of mucedo, and of its death and decomposition, the 
colouring matter remaining. 

II. Of Eggs kept at a Temperature of about 32° Fahr. 

On the 24th of June, four newly laid eggs were put into an ice-house, where 
they were left until the 19th of July. Cracks were found in two of them when 
taken out, but without any exudation of contents. These cracks might denote the 
freezing of the eggs. Put under a hen on the evening of the 17th, with nine fresh 
eggs, the latter were hatched on the 10th of August, as was also one of the former ; 
the two cracked eggs were crushed. The fourth from the ice-house, when broken 
was found to contain a mixture of yolk and white in the form of emulsion, with 
some unmixed yolk in a thickened state. The contents had an unpleasant smell, 
as if from incipient putrefaction. 

III. Of Eggs subjected to the Air-Ptcmp. 

1. On the 14th of April six newly laid eggs were thus treated until the 23d. 
The air-pump was in good order, and it was worked twice or thrice daily. On 
the 23d, these eggs were put under a hen with seven newly laid ones. The hatch- 
ing began on the 13th of May ; on the 14th all were hatched with the exception 
of one, — one of those subjected to the air-pump : this egg swam in water ; had, 
when broken, an unpleasant smell, denoting incipient putrefaction ; and the white 
and part of the yolk were mixed, forming a yellow opaque emulsion. There was 
an obscure appearance of an embryo in that portion of the yolk which was re- 
tained in its membrane. The newly laid eggs were hatched a few hours earlier 
than those acted on by the air-pump. 

2. Three newly laid eggs, on the 28th of May, weighed as follows : — 

No. 1 weighed 874-8 grs. i No. 3 weighed 953-0 grs. 
2 ... 912-0 „ 

They were subjected to the air-pump until the 2d of June, when, on weighing, 
they were found to have sustained the following loss : — 

No. 1, ... 4-8 grs. I No. 3, ... 5-1 grs. 
2, ... 4-0 „ 

They were put into water, and again subjected to the air-pump, which was worked 



344 dr john davy's 

twice or thrice daily. Taken out on the 18th of June, they were found to have 
gained as follows : — 

No. 1, ... 8.2 grs. I No. 3, ... 11-3 grs. 
2, ... 8-3 „ I 

They were now put under a hen, with seven newly laid eggs. On the 9th of 
June all the seven were hatched, but neither of the three. 

No. 1, when weighed, was found to have lost 308 grs. It sank in water. No 
traces could be detected in it of an embryo. It contained a bright yellow emulsion, 
a mixture of yolk and white, free from any unpleasant smell, of specific gravity 
1036 ; it was neutral to test papers. The chalazse and membranes were shrunk 
together. 

No. 2 had sustained a loss of 81 grs. Air procured from it was found to con- 
sist of about 18 per cent, carbonic acid, 82 azote. Its contents were very offensive 
and putrid, liquid and greenish, with a dark green clotted sediment. This under 
the microscope exhibited corpuscles, varying in diameter from 1500 of an inch 
to 1000; they were nearly circular, and contained greenish nucleoli. 

No. 3 had sustained a loss equal to 81-6 grs. It contained a yellowish emul- 
sion of specific gravity 1035. Some of its white still remained in its membrane 
in a thickened state. The fluid part had a putrid smell, but less offensive than 
the preceding. 

3. On the 23d of June four newly laid eggs weighed as follows : — 

No. 1 weighed 966-1 grs. I No. 3 weighed 886-8 grs. 
2 ... 7864 „ 4 ... 8304 „ 

They were put into water the same day — water deprived of air by the air- 
pump — and were subjected to the action of the pump. No air came from the 
water, but a good deal from the eggs. The pump was worked daily. On the 
25th of June a little air still continued to be given off from the eggs. On the 27th 
there was a cessation ; nor until the 19th of July did any more appear ; then 
two or three bubbles were seen to rise from one of the eggs. Now taken out and 
weighed, they were found to have gained as follows: — 

No. 1, ... 7-3 grs. No. 3, ... 7'6 grs. 



2, ... 7-0 



4, ... 8-2 



No. 1 was broken for examination. Its white appeared rather more liquid than 
common. Its specific gravity was 1033. The cicatricula seemed somewhat 
enlarged. The yolk was not apparently altered. There was no unpleasant smell 
either from the white or the yolk. On the exterior of its shell, and of the shell 
of the other three, there were minute opaque white spots, with a central aper- 
ture, distinguishable by the naked eye ; the spots were a little depressed. The 
appearance was suggestive of solution by a current of air (carbonic acid?) from 



OBSEEVATIONS ON INCUBATION. 345 

the egg under the action of the air-pump. They were mostly in the big end, but 
they were not confined to that end. 

The remaining three eggs were put under a hen with ten recently laid. The 
latter were hatched on the 11th of August. Of the eggs subjected to the air- 
pump, No. 4 only was hatched, and only about four or six hours later than the 
ten. The chick was healthy. The two aborted eggs were found to have lost as 

follows: — 

No. 2, ... 53-9 grs. | No. 3, ... 3216 grs. 

Both sank in water. Of No. 2 the yolk and white were in part mixed ; a por- 
tion of the white was free and thickened. The contents had no unpleasant smell ; 
no embryo could be found. Of No. 3 the yolk and white were found distinct, each 
in its proper membrane. In neither of them was there any apparent change, 
except that the white seemed more liquid than usual. Neither had any offensive 
smell, merely that of a stale egg. 

IV. Of Eggs kept in Lime Water. 

1. On the 17th of July three newly laid eggs were put into lime water, in 
which there was a great excess of lime. They weighed as follows : — 

No. 1 weighed 1024-5 grs. No. 3 weighed 937T grs. 

2 ... 900-5 „ I 

The vessel used, which was of glass, held little more than a pint ; it was full 
nearly to the mouth, and the mouth was only just large enough to admit the 
eggs. It was closed by a cork, and placed in a dark cupboard, where the tem- 
perature was about G3°, and subject to little variation. Taken out on the 17th 
of September (the water was covered with a crust of carbonate of lime), they 
were found to have gained as follows : — 



&* 



No. 1, ... 2-3 grs. No. 3, ... 40 grs. 

2, ... -6 „ J 

On the same day they were put under a hen with seven fresh eggs. Of the 
latter all but one were hatched on the 11th of October. This one, on receiving a 
blow, broke explosively, scattering wide its yellow, offensive contents; the 
explosion was nearly as loud as that of a pistol, showing how much the air it 
contained was compressed. Each of the eggs from lime water was unproductive. 
They were found to have lost as follows : — 

No. 1, ... 25-7 grs. I No. 3, ... 109 grs. 

2, ... Ill „ I 

All three sank in water. No. 1, broken under water, gave off two or three 
bubbles of air ; the quantity was too small for analysis. The yolk and white 
were distinct, but the former seemed unduly thin, as if from the admixture of 

VOL. XXIV. PART II. 5 A 



346 DR JOHN DAVY S 

some of the white. Both showed an alkaline reaction, but the white the 
strongest. The contents of No. 2 were similar. No. 3 was not examined. 

2. On the 26th of March thirteen eggs, which, when newly laid, had been 
placed in lime water,— some in the last week of February, some a few days later, 
but with less precaution than in the preceding trial, — were put under a hen. Of 
these one only was hatched, and on the 17th of April. The chick was healthy ; 
the rest all aborted. In five of them embryos were found more or less advanced ; 
in the other four no traces of an embryo could be detected ; their contents varied 
much in quality. Of one the yolk and white were distinct, each in its membrane, 
and so little altered, that the yolk retained its natural acid reaction, as well as 
the white its alkaline. The contents of the others were free from any marked 
putridity. 

V. Of Eggs in the Ordinary Process of Incubation. 

For the sake of comparison, I shall now notice briefly the results obtained in 
ordinary instances of incubation with eggs presumed to be impregnated, and 
which had in no way been interfered with. 

1. On the 27th of June thirteen eggs were put under a hen. Of these six were 
newly laid ; of the other seven, reckoning from the time of laying, 



No. 1 had been kept 36 days. 

2 ... 35 ., 

3 ... 34 ;, 

4 ... 33 „ 



No. 5 had been kept 31 days 

6 ... 29 ; 

7 ... 25 „ 



Of the six newly laid, three were hatched, three aborted. All three just swam 
in water ; one, opened under water, afforded a little air, which was found to con- 
sist of 20*6 oxygen, 794 azote. Each of them contained a well-advanced fetus. 

Of the seven, the numbers of which have been given according to the time of 
keeping or age, all but the first three were hatched, giving birth to healthy 
chickens. Of the unproductive three neither contained an embryo, or showed any 
signs of development. 

No. 1 contained a pale, thick, yellowish matter ; it had a smell like that of 
sour milk ; had an acid reaction ; was of the consistence of soft curd, and had 
much the same appearance. 

Of No. 2 the contents were liquid, with little viscidity ; of a richer yellow 
than the preceding ; had an alkaline reaction, and was of the specific gravity 1032. 
Distinct from the yellow liquid there was a small portion of glairy white. The 
contents of No. 3 showed no well-marked difference. 

The hatching in this instance was unusually prolonged ; the first chick 
appeared in the night of the 16th, the last of the seven in the night of the 18th. 
After that the hen deserted her nest, and may have been the occasion of the death 
of the advanced foetuses ; neither of them showed any signs of putridity. 



OBSERVATIONS ON INCUBATION. 347 

2. Of sixteen duck's eggs put under two hens in May, all but four were hatched. 
Of these four, two were found to contain each a foetus well advanced. In the 
other two there were no traces of development. Of one of these the white and 
yolk were distinct, and little altered ; of the other the white and yolk were com- 
mingled, very liquid, and had a slight disagreeable smell. It is worthy of remark, 
that there was a thick layer of mucor (M. mucedo) on the air vesicle of each of the 
eggs containing a foetus ; it was nearly black ; in a less degree it was found on 
the lining membrane of the shell of all three. Air from one of these eggs, equal 
in volume to "67 cubic inch, consisted of about 20 oxygen and 80 of azote. 

3. Ten eggs were put under a hen on the 24th of February. Three only were 
hatched. The seven unproductive eggs swam in water. In the first examined 
a foetus was found well advanced ; the fluid brownish and offensive. In the 
second the yolk and white were mixed, of a yellow colour, curdly, and offensive. 
In the third the contents were similar, but only slightly offensive. In the fourth 
they were more liquid, not curdly, very slightly offensive. In the fifth the yolk and 
white were only partially mixed, of a bright yellow, and not offensive. In the 
sixth there was a foetus about one quarter the size of that of the first ; the yolk 
and white mixed, of a dirty yellow, and offensive. In the seventh there was also 
a foetus ; it was less advanced than that of the first, but more than that of the 
last ; the yolk was brownish-yellow, the white gelatinous and transparent ; both 
offensive. 

VI. Conclusions. 

What are the conclusions to be drawn from the foregoing results? The 
changes experienced in the egg, as described in the several experiments, are so 
many and various, and the difficulty of referring them to their causes is so great, 
that I have much hesitation in drawing any decided inferences from them, espe- 
cially as regards suspension of vital action, in the trials, whether with the air- 
pump, lime water, or ice-house, in which incubation was afterwards successful. 

In the various experiments, it may be said that the whole of the oxygen was 
not withdrawn from the eggs, that a minute portion remained sufficient to main- 
tain a very low degree of vitality, enough, at least, to place in equilibrium for a 
time the antagonistic agencies — those administering to life and death. I shall 
relate one experiment which seems favourable to this view. On the 13th of May 
three newly laid eggs were put into water sufficient to cover them, and, with a 
piece of phosphorus placed by the side of the containing vessel, were subjected to 
the air- pump until the 28th. After the greater portion of the air had been ex- 
tracted from the water and the eggs, the phosphorus ceased to shine until the 
instant that the pump was worked (it was worked twice or thrice daily, and was 
in good order) ; then there proceeded from it flashes of light, lighting up the 
interior of the bell-glass, suggestive of its vapour being diffused through the 



348 DR JOHN DAVY'S 

aqueous vapour filling the receiver, and of the disengagement of a little air from 
the eggs, the cause of the combustion or luminous appearance. Not until the 
last night was there a cessation of the phenomenon. On the following day, the 
28th, the eggs, with a certain number of fresh eggs, were put under a hen: 
owing to an accident, the hatching process was interrupted. After an incubation 
extended to the 20th of June, one of the three eggs was found to contain a foetus ; 
the other two, in an unknown maimer, had been taken from the nest. That in 
this instance a very minute portion of oxygen might have remained in the egg 
— a portion not exhausted by the air-pump — seems not improbable. Thus much 
granted, there seems little difficulty in admitting the persistence of a feeble action 
in the egg in question, and this a vital action, similar to that which, it may be in- 
ferred, is in progress in the ordinary egg when in a fit state for hatching — a con- 
dition limited as to time, and in the common fowl seldom exceeding thirty days. 
If considerations of this kind render the results obtained from the vacuum 
eggs inferentially questionable, they are not less applicable to the results of the 
trials of the eggs kept in lime water and the ice-house. Under lime water access 
of air only is excluded. The little air in the egg may suffice for sustaining a very 
feeble action, sufficient for the preservation of life for a limited time. In an ice- 
house, at a temperature of 32°, or lower, if not low enough to freeze the egg, 
action may be diminished seemingly, but not be really arrested. The ova of the 
salmon, it has recently been ascertained, are capable of being hatched after 
having been kept in ice-water one hundred and twenty days, and thus conveyed 
to Australia. Whether there can be life without action, or its equivalent change, 
is a problem which I hardly venture to approach. In the seeds of certain vege- 
tables, which, circumstances not favouring, remain without germinating months 
and years, there seems to be during the period an arrest of vital force or action ; 
and yet, may it not be more apparent than real ? When we reflect that each 
kind of seed, like each kind of egg, has its term of retension of vitality — the 
longest, in the instance of the seed, little exceeding thirty years — we may be 
allowed to have our doubts on the subject. It is possible that during the whole 
period, however long, there may be a very feeble action, though imperceptible, 
sustaining life. It may be well to reflect on the coarseness of our measures of 
time, and that great cosmic changes, which require hundreds and thousands of 
years to become conspicuous, are produced by causes in continued operation, 
which are absolutely inappreciable in their momentary effects. An instance of 
this is afforded by the worn-foot of the bronze statue in St Peter's, so worn by 
the kisses of devotees during hundreds of years. What we witness in certain 
hibernating animals seems to favour our doubts. In the instance of the dormouse, 
in the depth of winter, there are no distinct indications observable of life; its 
temperature is about that of the air ; no arterial action is perceptible ; yet it 
would appear that the heart's action, and the action of the secreting organs, is not 



OBSERVATIONS ON INCUBATION. 349 

absolutely suspended. Even congelation itself, it may be conjectured, may be 
compatible with the retention of a low vital force, more or less morbid or de- 
ranged ; at least, congelation, I have found, does not entirely arrest action in the 
blood, ammonia being formed in it, and evolved from it when frozen.* 

Relative to the varied changes witnessed in the aborted or unproductive eggs 
— some amounting to putrefactive decomposition, some indicative of the forma- 
tion of new compounds, some so inconsiderable as to be only just appreciable — it 
is difficult to offer any satisfactory explanation, especially as, in every instance of 
incubation, all have been apparently very similarly acted on. Mr Hunter has 
expressed the opinion that eggs which have " not hatched become putrid in 
nearly the same time with any other dead animal matter, f This statement is 
not supported by the preceding results. At one time I was disposed to infer, 
from various experiments I had made, some of which are to be found in the last 
volume of my " Physiological Researches," that the circumstance which most 
favours the putrefactive change in the egg is the commingling of the white and yolk. 
But from later experiments, especially one recently made, my confidence in this 
opinion has been shaken. The experiment was the following : — Eight newly laid 
eggs were wrapped in paper, placed in a basket, and covered with paper, in a 
room, the temperature of which ranged from about 50° at night to 55° by day. 
The placing them was begun on the 27th of November, and continued as follows, 
each egg being weighed at the time : — 



No. 1, November 27, weighed 831 3 grs. 

2, ... 28, ... 9910 „ 

3, ... 30, ... 8425 „ 

4, December 2, ... 8934 „ 



No. 5, December 5, weighed 890 - 5 grs. 

6, ... 8, ... 862-4 „ 

7, ... 10, ... 8690 „ 

8, ... 13, ... 1012-5 „ 



They were left undisturbed until the 30th of January, when they were taken out 
and again weighed. 



No. 1 was found to have lost 2 - 4 per cent. 

2 3-2 „ 

3 ... ... 3-5 

4 3-3 „ 



No. 5 was found to have lost 29 per cent. 

6 30 „ 

7 30 

8 2-2 „ 



These eggs were now put- under a hen with five fresh ones. On the 28th of 
February the latter were all hatched ; the former were found to have failed. 



No. 1 had sustained a further loss of 1 58 per cent. 

2 144 „ 

3 138 „ 

4 ... ... 16-6 „ 



No. 5 had sustained a further loss of 147 per cent 

6 122 „ 

7 121 „ 

8 ... ... 58 .. 



This trial was made on the idea that, by checking evaporation, and by perfect 

* See Transactions Roy. Soc. of Edin. vol. xxiv. p. 26. 
f Philosph. Trans, for 1778, p. 29. 

VOL. XXIV. PART II. 5 B 



350 DR JOHN DAVY'S OBSERVATIONS ON INCUBATION. 

rest, a retardation might be effected of the changes unfavourable to life, and that 
it might be indicated by some traces of vital development in the eggs. But the 
results were all of the contrary kind ; in no one of the eggs were there any marks 
of development. Two of them, No. 4 and No. 8 — the one which had sustained 
the greatest loss during incubation, the other which had % sustained the least — 
were opened under water. The air from No. 4, a little more than half a cubic 
inch, was found to consist of 1 per cent, carbonic acid, 19 oxygen, 80 azote ; 
whilst that of No. 8, somewhat less in quantity, consisted of 2*5 carbonic acid, 
5 oxygen, and 925 azote. The contents of the two differed considerably. Those 
of No. 4 were a mixture of yolk and white, forming a yellow fluid, of little 
viscidity, of no unpleasant smell, of faint alkaline reaction, and giving off with 
quicklime a slight smell of ammonia. The contents of No. 8 had an offensive 
smell, approaching the putrid, a duller colour, a more distinct alkaline reaction, 
and mixed with lime, a stronger ammoniacal odour. The contents of the other 
eggs, with the exception of No. 7, were found to resemble very much No. 4. 
They had no unpleasant smell, and, if anything, they were of a brighter yellow, 
and of feebler alkaline reaction. No. 7 had undergone a greater change ; its con- 
tents were of a greenish-mottled hue, nowise viscid, of unequal consistence, par- 
tially curdled, of a very offensive putrid smell, strong alkaline reaction, and with 
lime emitting a strong smell of ammonia. Under the microscope it was seen to 
consist of very fine granules and of globules or cells, like those of a mucedo, in 
which, it may be inferred, that the colouring matter existed. Now, as in all 
these eggs, excepting one, putridity had not taken place, though the yolk and 
white had become intimately mixed, and were exposed to a temperature favour- 
able to the change, it seems pretty evident that a mere admixture of the two is 
not adequate to excite the putrid fermentation, and that something else is essen- 
tial. But what that something is, I cannot at present venture to conjecture. It 
seems to me that the putrefaction of the egg, as regards its vera causa, is as yet 
nearly as much unsolved as that of the coagulation of the blood, and, like it, may 
perhaps be considered as belonging to the great mystery of life and death. 



PLATE XXIV. 



Jferui Daily Curves nl the six Summer and the six Winter Months of 1826 X- J/127. 



A.M. 



'Ihins Uqy. Soc "Edinburgh V6L. Z&IV pag&356 



i n 


in iv 


V 


vi vn vm rx x xi xii i n 


m 


IV 


v vi vn vie ix x xi 


xn 
















































































































































































































































































61 






































































































































60 
59 
58 
57 












































































































































^s. 






















































\ 


\\ 
































/ 




















\\ 














55 
54 
53 


















/ / 
























v 


























/ 

/ 


/ / 


























v S 






























z 












































































































1827 




52 


\i turner 


. 


























































\ 


1826 




Curve 




























, 






































51 








































- 






























































































50 
49 




































X 


V. 


















































































































































48 




































































182 7 






























































1826 




47 
46 
45 


Summer 
Curve 
















































1827 
























































| I 

J 






















































44 
43 








































































, 1827 


































































42 


Kilter 


-- . 


















































~~~ 


^**^^ 


;><-- 






1826 
























-""C* 








































1827 




41 
40 
39 
38 

37 


1826 




















































































































u 





















































36 

35 
34 
33 


:_ 


[ T 


[ n 


i n 


r \ 


' VI VI 


I VI 


n e 


I 3 


: x 


[ xn i 


r 


[ I 


[{ 


L\ 




v 


V 


[ V 


1 VI 


a r 


s: s 


: x 


[ X 


a. 






AM 








P.M. 












W.&AJLJahiubm ii!u:' 


. 





































































PLATE XXV 1 



Mean Dnilv Curves for eaeh Month of 1826'. 



AM. 
























P.M. 














Trav us. 'Ray. Soo 


Edmburtjh Vol JUY page£56 


i n in iv 


v vi vn vm ix x xi xn i n 


m iv v vi vn vm rx x xi xn 
























































65 
64 
63 
6Z 
61 
60 
59 

as 

57 
56 
55 
54 
53 
5Z 
51 
50 
49 
48 
47 
46 
45 
44 
43 
42. 
41 
40 
39 
38 
37 
36 
35 
34 
33 
































/ 
































































































/ 














































































































/ 


/ 






























































^ -^ 




































/ 


/ 
























































/ 














■ 


^^ 










\ 


Aug 




. hu! 












/ 






/ 






































\, 












/ 


/ 


















































/ 
































Sep. 

June. 




Sep 
Juhl 












f / 


_ ' . 


/ 






/ 










\ 
















July 
















/ 


/ 








/ 










\ 
































/ 
























■^ 






























/ 










\ 




- 








— J 






























/ 








S 


' 


























Oct 
















/ 






X 

/ 
















\ 








\ 




Oct . 






















/ 






























May 






































































/ 












"' 














































' 


/ 


























April 




: 












/ 




























































/ 




































Dec 
Feb 
















































Mm rh 




























/ 


7 












































-^ 










































Nov 


































































































































/ 




















































































-,_ 
















































Jan,. 




.Inn 






































































































' A 


i n m iv 


v vi vn vm ix x xi xn i n 


m iv ^ 


r vi vn vm ix x xi xn 




jjt. 
























P. 


M. 






















.! 


, I h 


r '. 


n ~Ede:n y ~ 



PLATE XXV - 2 



AM. 



Mian Daily Curves for each Month, of* 1827. 
V M 



Traiis.l&cn. Sue. EdJitbiugK. Tol. JlXL^ p<uoe358 



I TL 


HE IV 


"v yi yk vnr ix 


X 


xr xir i n 


hl iv 


t n tit 7nr ix 


x xr xn; 
























































65 
64 
63 
6Z 
61 
60 
59 
58 
57 
56 
55 
54 
53 
5Z 
51 
50 
49 
48 
47 
46 
45 
44 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
33 




























































































































































































































































































y y 


^ 
























































































































\ 










■Tidy 










































" 










Sep. 




July 




— - 












/ 


























\ 










Aug. 










































\ 






Aug 




























































Oct . 














































\ 


June. 

net. 








■^^ 




































































































































































May 




Mi it/ 






















/ 
































































\ 


\ 




















































































/ 
/ 






















































/ 


/ 




































Nov 
April 














/ 










y 
























Apri]\ 

'Nov. 

Dec. 




















s' 






































































































































































y 


































.M'ltdi 




Mn rrh 










































































s' 


























Jiuv. 














































































































Feb. 










































































































































































nr it 


t "7t w Tnr k 


X 


xc xir ] 


[ n 


m ip 


t w w vnr is 


x xi xrc 





A.M. 



PM. 



VKtLAKJohnstnn. EJin!' 



351 



XXVII. — Report on the Hourly Meteorological Register kept at Leith Fort in the 
Years 1826 and 1827. By Sir David Brewster, K.H., D.C.L., F.R.S. 
(Plates XXIV. and XXV.) 

(Bead 19tli February 1866.) 

Having already published in the Transactions* a detailed report on the 
Hourly Meteorological Register kept at Leith Fort, at the expense of the Society, 
during the years 1824 and 1825, it is unnecessary to enter into any recapitula- 
tion respecting the origin and history of this class of observations. 

The singular and unexpected results obtained from these Registers, and the 
rapid approximation to general laws which some of these results exhibited, 
attached a great interest to the observations of future years ; and it is satisfac- 
tory to find that the results for the two following years of 1826 and 1827 are 
almost perfectly coincident with those for 1824 and 1825, not only in their 
general relations, but even in their numerical laws. 

The following are the Mean Temperatures of the four years during which the 
hourly observations were made at Leith Fort : — 

Mean Temperature of 1824, ...... 47588 

of 1825, 48-911 

of 1826, 48-436 

of 1827, . . . • . . 48-407 

Average Mean Temperature of four years, .... 48-335 

The following Tables contain the mean temperatures for every day of the 
year, and for every hour of the day for 1826 and 1827: — 

* Vol. X. p. 362. 



VOL. XXIV. PART II. 5 C 



352 



SIR DAVID BREWSTER ON THE HOURLY 



MEAN RESULTS OF THE HOURLY REGISTER FOR 1826. 



The Mean Temperature of the Winter Months, viz. Dec. Jan. Feb. is 

,, ., of the Spring Months, viz. March, April, May, . 

,, ,, of the Summer Months, viz. June, July, August, 

,, ,, of the Autumn Months, viz. Sept. Oct. Nov. 

The Mean Temperature of the Year 1826, from 8760 observations, is 



40556 
46135 
58263 
48818 

48-436 



TABLE I. — Containing the Daily and Monthly Mean Temperatures for 1826. 



Day. 


January. 


Feb. 


March. 


April. 


May. 


June. 


July. 


Aug. 


Sept. 


Oct. 


Nov. 


Dec. 


1 


32-94 


40-40 


4549 


46-48 


44-65 


5409 


62-04 


56-77 


56-46 


56-44 


43 54 


39-29 


2 


3777 


43-82 


41-40 


46-55 


4903 


49 88 


61-66 


52-96 


58-57 


5269 


43-21 


40-38 


3 


39-42 


47-92 


42-28 


51-29 


42-57 


51-33 


61-96 


56-50 


58-35 


51-78 


41-67 


36-38 


4 


3734 


43-26 


42-38 


49-65 


43-09 


52-84 


60-47 


56-58 


5790 


4755 


43-62 


35 00 


5 


3654 


4321 


3915 


50-21 


45-75 


52-69 


6094 


56-20 


53 25 


45-06 


46-41 


31-51 


6 


36-21 


47-54 


41-59 


50-40 


43-00 


58 88 


62-50 


5600 


53-58 


4773 


3908 


32-75 


7 


36-16 


42-77 


43-22 


49-33 


45-55 


53-97 


60-58 


59-97 


56-82 


55-53 


3908 


41-99 


8 


30-69 


46-84 


44-08 


53-87 


44-38 


54-92 


62-26 


58-42 


5404 


48-02 


3909 


44 09 


9 


24-36 


47-34 


54-57 


50-27 


44-26 


49-00 


5631 


54-86 


5268 


45-96 


38-37 


44-31 


10 


3098 


43-55 


59-20 


46-01 


48-40 


50-80 


57-47 


54-25 


54-20 


48-24 


44-22 


46 92 


11 


3126 


39-08 


50-57 


48-17 


4749 


54-33 


57-77 


55-86 


55-15 


51-27 


50-29 


50-01 


12 


29-45 


4375 


43-92 


47-50 


48-16 


6035 


55-46 


56-15 


56-50 


51-16 


41-80 


48-91 


13 


25-49 


45-60 


41-26 


46-31 


51-72 


62-35 


56-47 


60-40 


5902 


5041 


39-11 


46-76 


14 


20-94 


43-31 


39-65 


49-72 


5386 


5745 


52-38 


6217 


54 36 


49-15 


37-71 


44-25 


15 


22-03 


46-26 


41-18 


46-97 


54-38 


54-88 


53-85 


6196 


50-82 


5605 


38-72 


45-15 


16 


24-01 


46-79 


39-06 


46-10 


49-90 


51-51 


55-36 


60-51 


56-55 


54-85 


35-42 


4442 


17 


40-79 


42-04 


38-88 


46-99 


54-78 


55 14 


54-42 


61-58 


60-25 


52-37 


39-15 


4405 


18 


43-75 


37-00 


43-48 


47-65 


57-67 


56-99 


56-60 


69-75 


53-07 


48-26 


37*65 


4316 


19 


34-94 


38-75 


42-36 


50-67 


52-54 


55-34 


54-34 


68-23 


55-01 


48-55 


41-09 


3886 


20 


40-15 


39-17 


44-24 


53-73 


49-32 


57-47 


51-44 


62-44 


54 09 


52-76 


39-00 


39-99 


21 


43-30 


41-55 


43-22 


49-80 


52-27 


5463 


50-42 


59-72 


51 99 


5471 


39-70 


37-46 


22 


39-21 


48-06 


39-65 


49-27 


53-71 


52-27 


5014 


57-94 


52-16 


54-21 


42-97 


45-29 


23 


40-32 


39-65 


39-44 


44-45 


48-90 


56-52 


50-16 


63-74 


51-21 


5611 


45-38 


47-66 


24 


3776 


43-15 


39-22 


4316 


49-75 


6511 


53-94 


63-53 


52-87 


56-05 


38-94 


4760 


25 


40-95 


43-67 


36-92 


41-17 


51-31 


68-79 


57-60 


63-28 


53-90 


50-91 


35-87 


44-96 


26 


3815 


41-78 


36-71 


42-11 


46-32 


69-34 


5801 


60-04 


60-08 


4509 


34-52 


4012 


27 


38-37 


41-35 


40-60 


35-91 


50 28 


6411 


61-80 


60-26 


5905 


48-12 


31-48 


39 17 


28 


4009 


47-78 


44-91 


35-30 


51-47 


6701 


64-20 


59-87 


55-00 


4786 


38-99 


4265 


29 


41-16 




37-22 


37-85 


50-48 


64-31 


6209 


64-15 


58-57 


47-55 


42-72 


45-12 


30 


4372 




38-26 


41-44 


50-79 


64-66 


6246 


61 94 


61-31 


45-87 


43-88 


47-67 


31 


44-42 




41-46 


... 


5113 




61-69 


5767 




4426 


... 


47-58 


Mean -\ 
Temp. 1 
of each r 


35-570 


43-407 


42-438 


46-611 


49-269 


57365 


57-633 


59-792 


55-561 


50-470 


40-423 


42-692 


Month. ) 



























The Mean Temperature of 1826 is, by this Table, 48°436. 



METEOROLOGICAL REGISTER KEPT AT LEITH FORT IN 1826 AND 1827. 



353 



TABLE II. — Showing the Mean Temperature op each Hour for each Month in 1826, 

AND FOR THE WHOLE YEAR. 



Hour. 



January. 



1 A.M. 

2 ... 

3 ... 

4 ... 

5 ... 

6 ... 

7 ... 

8 ... 

9 ... 

... 

1 ... 

2 .. 

1 P.M. 

2 ... 

3 ... 

4 ... 

5 ... 

6 ... 

7 ... 

8 ... 

9 ... 

... 

1 ... 

2 ... 



Feb. 



33822 
33927 
33-926 
33-880 
33890 
33-890 
33-863 
34T69 
35-024 
35952 
36661 
37-557 
38-210 
38-274 
38-200 
37-677 
36-758 
36-202 
35-798 
35-476 
35-363 
35-226 
34-903 
34-702 



41 

41 
41 
41 
41 
41 
42 
42 
43 
44 
44 
44 
46 
46 
4G 
45 
44 
43 
43 
43 
42 
42 
42 
42 



March. 



•723 
•812 

562 
•822 
•750 
•732 

009 
•281 
•527 
•277 
•795 
•973 
•134 
•295 
•170 
•402 
•661 
•920 
•553 
■286 
•857 
•678 
•420 
•312 



40492 
40-089 
39960 
39-855 
39-331 
39-355 
39-516 
40-468 
41-806 
43 331 
44-258 
45-290 
45-758 
46-169 
46081 
45-645 
45-476 
43-935 
43-072 
42516 
41-984 
41-540 
40-911 
41 000 



April. 



43650 
42 975 
42-700 
42433 
42-358 
42-925 
43958 
45358 
47075 
48125 
48-958 
49-985 
50-400 
49-917 
50208 
50-650 
50-692 
50-475 
48-433 
47-108 
46-283 
45-675 
44-800 
44-017 



May. 



45-234 
44-645 
43-822 
43-710 
44-153 
44-968 
46-145 
47-661 
49-572 
50-322 
51-500 
52-274 
53-065 
53-581 
53-613 
53-992 
53-903 
53-879 
52-306 
50-693 
49-548 
48-540 
47-701 
47-298 



June. 



July. 



52-833 
51-975 
51-367 
51-225 
51-700 
52-725 
53 917 
55-358 
57-075 
58-400 
60-150 
61-150 
62-192 
62-425 
62-650 
63-092 
63367 
62858 
61-417 
59-025 
56-975 
55-908 
55-183 
54-033 



53-274 
52-927 
52-871 
53-008 
52742 
53-863 
55-250 
56-685 
58-161 
59-282 
60-073 
60-806 
61-427 
62-185 
62-282 
62-540 
62-653 
62-428 
61-000 
58-057 
56-589 
55726 
55-387 
54-492 



Aug. 



56-790 
56-274 
55-645 
55-427 
54-863 
55-847 
57-307 
58-307 
59-363 
60-597 
61-766 
63-057 
63-347 
63-726 
63-920 
64-468 
64-137 
63912 
62645 
60-813 
59-476 
58-670 
58-210 
57-670 



Sept. 



Oct. 



53-125 
52767 
52-267 
52-242 
51 808 
51-833 
52-750 
53-750 
55-325 
56-917 
58-400 
59-167 
58-973 
59-333 
59-300 
59-557 
59092 
57-807 
56-358 
55683 
54-792 
54-323 
54-067 
53-633 



Nov. 



48-3(53 
47-976 
47863 
47960 
48-057 
47960 
48000 
49-129 
50-807 
52-379 
51-984 
53863 
54-153 
54-162 
54-065 
53-516 
52-411 
51-121 
50-540 
50-307 
49-508 
49-097 
48-677 
48-484 



Dec. 



39-242 
39T00 
39125 
39-142 
39-283 
39-383 
38-992 
39-550 
40008 
40-685 
41-640 
42-433 
42-790 
42-907 
42-617 
42-017 
41-433 
40-717 
40-342 
40-067 
39-873 
40-000 
39-773 
39-692 



42-193 
42-089 
42-145 
41-976 
41-742 
41-605 
41-653 
41-935 
42- 145 
42-693 
43-395 
43-670 
43-943 
44161 
43-853 
43-605 
43-415 
43-307 
43-057 
42-847 
42-532 
42-379 
42T37 
42-121 



Mean Temp, 
of each Hour 

for the 
whole Year. 



45-916 
45565 
45-289 
45-240 
45 154 
45-525 
46-133 
47-075 
48-347 
49-438 
50-407 
51-214 
51-724 
51-958 
51-941 
51-879 
51-533 
50-915 
49-910 
48-851 
48-008 
47-504 
47-036 
46-670 



The Mean Temperature obtained from the last column in the above Table is 48M68. 
It occurred at 9 h 7 m a.m. and 8 h 27 ra p.m. 



354 



SIR DAVID BREWSTER ON THE HOURLY 



HOURLY REGISTER FOR 1827. 



The Mean Temperature of the Winter Months, viz. Dec. Jan. Feb. is 
„ ., of the Spring Months, viz. March, April, May, 

„ „ of the Summer Months, viz. June, July, August, 

„ „ of the Autumn Months, viz. Sept. Oct. Nov. 



The Mean Temperature of the Year 1827, is 



38-945 
45817 
57-612 
51-255 

48-407 



TABLE III. — Containing the Daily and Monthly Mean Temperatukes for 1827. 



Day. 


January. 


Feb. 


March. 


April. 


May. 


June. 


July. 


Aug. 


Sept. 


Oct. 


Nov. Dec. 


1 


43-68 


37-64 


41-70 


48-79 


47-61 


54-50 


56-92 


61-67 


56-09 


56-48 


41-71 


45-29 


2 


2822 


35-60 


34-63 


50-99 


51-25 


52 


36 


55-58 


62-69 


59-35 


54-43 


48-31 


43-25 


3 


20-44 


33-29 


33-34 


5036 


53-23 


49 


80 


57-59 


61-83 


57-73 


55-75 


49-38 


46-67 


4 


2826 


3627 


32-86 


48-53 


5484 


52 


34 


59-47 


56-80 


55-79 


54-71 


48-30 


53-14 


5 


27-85 


41-22 


33-77 


51-13 


52-11 


50 


71 


59-99 


5905 


56-69 


52-57 


48-62 


50-49 


6 


44-88 


40-05 


38-50 


48-34 


46-39 


51 


91 


61-62 


55-41 


55-51 


56-58 


43-60 


40-73 


7 


48-97 


37-90 


32-76 


46-85 


44-83 


53 


15 


59-41 


58-82 


56-72 


5406 


4300 


4538 


8 


48-95 


35-98 


30-34 


47-87 


4714 


57 


37 


62-71 


59-31 


5650 


52-51 


44-27 


42-48 


9 


38-66 


35-45 


32-96 


49-05 


47-95 


61 


23 


5937 


61-67 


5869 


54-08 


50-18 


43-95 


10 


38-75 


38-72 


36-46 


4612 


43-42 


61 


23 


57-75 


57-43 


62-89 


4811 


49-26 


49-56 


11 


32-31 


3793 


41-84 


44-39 


45-95 


61 


34 


56-58 


5592 


63-56 


5065 


43-89 


46-69 


12 


29-38 


3626 


41-99 


47-58 


50-93 


60 


87 


57-17 


5-5-14 


5701 


50-52 


49-25 


40-91 


13 


40-48 


3513 


40-67 


4731 


5418 


57 


56 


57-61 


56-95 


55-75 


48-35 


55-23 


40-75 


14 


40-97 


36-13 


39-58 


48-53 


49-19 


57 


63 


57-09 


53-76 


58-62 


48-37 


53-33 


44-96 


15 


35-25 


32-41 


37-10 


47-81 


48-72 


56 


12 


60-30 


52-54 


62-62 


56-58 


43 13 


45-12 


16 


38-92 


30-36 


40-27 


45-74 


48-58 


61 


45 


65-01 


51-35 


63-91 


58-01 


46-29 


41-85 


17 


35-46 


31-24 


42-78 


44-53 


51-66 


57 


98 


65-37 


5386 


62-68 


55-53 


4410 


45-43 


18 


37-21 


28-35 


38-72 


4208 


48-53 


56 


66 


59-78 


53-38 


55-61 


51-98 


36-44 


4319 


19 


3744 


28-69 


47-42 


42-93 


54-46 


54 


33 


56-59 


55-12 


49-98 


53-98 


38-44 


46-59 


20 


3532 


31-58 


47-15 


43-01 


53-37 


50 


88 


55-46 


54-42 


56-53 


5404 


44-42 


41-98 


21 


35-96 


35-09 


47-65 


42-38 


5912 


52 


59 


56-10 


57-86 


56-66 


53-24 


33-48 


43-08 


22 


3537 


33-30 


50-71 


40-69 


56-89 


53 


23 


58-33 


5587 


57-46 


50-05 


31-58 


41-34 


23 


3313 


35-92 


51-91 


35-54 


54-75 


53 


77 


59-58 


58-55 


57-50 


50-15 


33-08 


40-41 


24 


34-01 


36-21 


46-14 


34-65 


5676 


54 


95 


64-58 


57-57 


5622 


53-26 


32-35 


46-47 


25 


36-11 


35-85 


38-69 


37-53 


50-46 


57 


63 


61-54 


55-58 


5756 


54-02 


38-83 


45-97 


26 


35-77 


4605 


40-17 


41-39 


51-03 


58 


16 


56-64 


54.87 


56-50 


55-12 


42-71 


5088 


27 


30-96 


40-41 


45-12 


45-75 


51-21 


58 


60 


59-73 


59-81 


55-42 


52-51 


47-98 


4566 


28 


45-73 


37-36 


40-61 


47-49 


54-66 


58 


53 


62-72 


56-96 


54-95 


43 96 


49-98 


4072 


29 


48-19 


... 


3812 


50-25 


56-35 


58 


02 


63-53 


56-21 


5586 


43-46 


48-45 


32-67 


30 


45-26 


• ■ • 


40-55 


51-25 


57-02 


5798 


62-67 


59-61 


55-61 


46-69 


47-33 


30-62 


31 


4352 




42-15 


... 


57-26 




63-97 


5815 


... 


42-65 




42-69 


Mean ~\ 
Temp. 1 
of each t 


37-271 


35-728 


40-215 


45-628 


51-608 


56-096 


59-702 


57-037 


57-532 


52-013 


44-221 


43836 


Month. ) 























































METEOROLOGICAL REGISTER KEPT AT LEITH FORT IN 1826 AND 1827. 



355 



TABLE IV. — Showing the Average Mean Temperature of each Hour for each Month 

IN 1827, AND FOR THE WHOLE YEAR. 



January. 



37-121 
37-097 
36-935 
36-734 
36-508 
36-532 
36-419 
36-701 
36-911 
37-250 
37-605 
38072 
38-129 
38-362 
38-282 
38064 
37-911 
37-564 
37-218 
37-153 
36968 
36-927 
37-008 
36-959 



Feb. 



34-982 
34-955 
35-080 
35-160 
34-768 
34-553 
34-643 
34-652 
35134 
35-768 
36-518 
37-375 
37-259 
37-625 
37-419 
37-089 
36616 
36-202 
35-785 
35-563 
35-330 
35-259 
35-321 
35-357 



March. 



38-508 
38-395 
38-290 
38-169 
37-855 
38185 
38-516 
39185 
40379 
41-201 
42387 
42-750 
43-395 
43-371 
42-927 
42-645 
41-935 
40-935 
39-958 
39-896 
39-605 
39193 
38-887 
39-024 



April. 



43-275 
42925 
42-500 
42-356 
42-508 
43-083 
43-291 
44-475 
45-608 
46-800 
48-041 
48-658 
49-016 
49-066 
49-183 
48-950 
48-300 
47-566 
46-541 
45-658 
45-041 
44-391 
44-050 
43-691 



May. 



48-718 
48-161 
47-750 
47-790 
48-072 
48-645 
49-492 
50-234 
51-218 
51-895 
53-145 
53-492 
54-185 
54-734 
54-879 
54-943 
54-943 
54-137 
53-709 
52-355 
51-750 
51-097 
50-314 
49-629 



June. 



52-091 
51-491 
51-016 
51-258 
51-850 
52-866 
54-066 
55-716 
57-075 
58121 
58783 
59-400 
59-975 
60-541 
60-725 
60-633 
60-400 
59-750 
58-191 
56-841 
55-341 
53-625 
53-541 
52-733 



July. 



56-056 
55-492 
54 863 
54-677 
55-201 
56-145 
57-605 
58-725 
60-105 
61-306 
62-153 
62-951 
63-589 
63-516 
63-806 
64-056 
63-363 
62951 
62-387 
61-185 
59-571 
58-274 
57-532 
57-209 



August. 



54-379 
53-685 
52-935 
52-693 
52-976 
53-306 
54-911 
56330 
57-355 
58182 
59-435 
60-290 
60-871 
61-161 
60-814 
60-669 
60-323 
59-863 
58-967 
57-669 
56-750 
56-048 
55-427 
54-597 



Sept. 



56-050 
55-608 
55-433 
55-241 
55-550 
55-800 
56-091 
56-850 
57516 
58-075 
58-650 
59-233 
59-641 
59-607 
59-966 
60-233 
60-283 
59-075 
58-558 
58-000 
57-300 
56-841 
56-891 
56-300 



October, 



52-597 
52-589 
52-403 
52-153 
51-903 
51-763 
51-677 
51-556 
51-580 
52-057 
52-476 
52-355 
52-193 
52-258 
51-968 
51-888 
51-637 
51-532 
51-516 
51-847 
52-161 
51-944 
52-201 
52-330 



Nov. 



43-550 
43368 
43-116 
43-000 
42-808 
42-733 
42-841 
43-008 
43-491 
44-183 
45-375 
46-400 
46908 
46-991 
46-600 
45-800 
45-458 
44-866 
44-616 
44-275 
44-075 
44-008 
43-900 
43-850 



Dec. 



Mean Temp 
of each Hour 

for the 
whole Year. 



43-282 
43-129 
43-185 
43-290 
43282 
43-322 
43 242 
43-411 
43-548 
44-008 
44-556 
45153 
45-201 
45-209 
44943 
44-339 
44-242 
43 830 
43-766 
43637 
43540 
43-242 
43-484 
43-589 



46-717 
46-408 
46-125 
46-043 
46-107 
46-411 
46899 
47-570 
48-327 
49-070 
49-927 
50-511 
50-863 
51037 
50 959 
50-776 
50-451 
49-856 
49-268 
48-673 
48-119 
47571 
47-379 
47-105 



The Mean Temperature obtained from the last column in the above Table is 48°-423. 
The Mean Temperature of 48°-423 occurs at 9 h 12 m a.m. and 8 h 23 m p m. 



VOL. XXIV. FART II. 



O I) 



356 SIR DAVID BREWSTER ON THE HOURLY 

The general results which may be deduced from the preceding Tables 
relate — 

1. To the form and character of the annual and monthly daily curves, or the 
daily progression of temperature. 

2. To the arrangement of the monthly curves in separate groups. 

3. To the determination of the times of the day when the mean temperature 
occurs. 

4. To the relation between the mean temperature of the day, and that of any 
single hour or pair of similar or homonymous hours. 

5. To the parabolic form of the four branches of the annual daily curve. 

I. On the Form and Character of the Annual and Monthly Daily Curves, or the Daily 

Progression of Temperature. 

The mean temperature of the year 1826 was 48°436, and that of 1827 48°-407, 
both of them intermediate between that of the two preceding years ; but though 
in its average character the temperature of 1826 was moderate, yet it differed 
from both of them in a remarkable manner. Though the mean annual curves of 
1824 and 1825 differ from one another, from the former representing a cold and 
the latter a warm year, yet they are perfectly parallel, indicating the same 
vicissitudes of climate. The curve of 1826, however, exhibits the character 
of an American climate, descending almost as low as that of 1824 in the 
morning branch, and rising nearly as high as 1825 in the warm period of the 
day. 

The curve for 1827 differs remarkably from that of 1826, keeping above it 
from 1 o'clock in the morning till 8 o'clock in the evening, but almost touching it 
at the morning and evening hours of mean temperature. See Plates XXIV. and 
XXV. ' 

In all the curves for these four years, the lowest temperature took place at 
5 o'clock in the morning. The temperature increased, with great regularity, till 
3 o'clock in the afternoon, when it descended to its minimum. The period, 
therefore, of its ascending is ten hours, and that of its descending motion fourteen 
hours. 

By comparing the summer and winter curves or the mean temperatures of 
the six summer months, from April to September inclusive, with those of the six 
winter months, from October to March inclusive, as exhibited in the annexed 
Table, we are enabled to discover whether or not the peculiar character of 1826 
is derived from the warm or the cold season. 



METEOROLOGICAL REGISTER KEPT AT LEITH FORT IN 1826 AND 1827. 357 



TABLE, showing the Mean Temperature op each Hour for the Six Summer 
Months, from April to September inclusive, and for the Six Winter Months, 
from October to March inclusive, for 1826 and 1827. 





1826. 






Six Summer 


Six Winte 


Hours. 


Months. 


Months. 


1 A.M. 


50818 


40 ? 972 


2 


50260 


40-832 


3 


50112 


40763 


4 


49667 


40772 


5 


49-604 


40-675 


6 


50-366 


40-654 


7 


51-554 


40-672 


8 


52-853 


41-255 


9 


54-428 


42-219 


10 


55-604 


43-219 


11 


56-808 


45123 


12 


57-740 


44-590 


1 P.M. 


58-234 


45-165 


2 


58-528 


45-271 


3 


58-662 


45-104 


4 


56731 


44-647 


5 


59-333 


44026 


6 


58726 


43-200 


7 


57-026 


42-727 


8 


55-229 


42-416 


9 


53-943 


42019 


10 


53141 


41-820 


11 


52-561 


41-470 


12 


51-857 


41-385 



Mean, 54324 



42-541 





1827. 




Hours. 


Six Summer 


Six Winter 


Months. 


Months. 


1 A..M. 


51°-761 


41°667 


2 


51-227 


41-589 


3 


50-749 


41-501 


4 


50669 


41-418 


5 


51026 


41187 


6 


51-641 


41181 


7 


52-576 


41-223 


8 


53-721 


41-419 


9 


54-813 


41-900 


10 


55-396 


42-411 


11 


56701 


43153 


12 


57337 


43684 


1 P.M. 


57846 


43-848 


2 


58- 104 


43-969 


3 


58-229 


43-689 


4 


58-247 


43-304 


5 


57-935 


42-966 


6 


57-224 


42-488 


7 


56-292 


42143 


8 


55-285 


42062 


9 


54-292 


41-946 


10 


53-379 


41766 


11 


52-959 


41-800 


12 


52-359 


41-851 



Mean, 54-574 



42-257 



The summer curve of 1826 retains the same intermediate position between 
those of 1824 and 1825 that it did in the annual curve; but in the morning 
hours it descends nearly to the curve of the cold year of 1824, while in the 
afternoon hours it rises towards the curve of the warm year 1825, thus display- 
ing, in the summer season, the character of an American climate. 

The summer curve of 1826 bears the same relation to that of 1827, keeping 
below it in the morning till about 11 o'clock, when it rises high above it till 8 
o'clock, when it descends till midnight. 

In the winter curves, that of 1826 keeps between those of 1824 and 1825 
from 1 o'clock a.m till 8 o'clock. It then rises above that of 1825, and keeps 
above it till 6 o'clock in the evening, when it again meets that of 1825, coinciding 
with it till about 3 o'clock in the morning. Hence it follows that the peculiar 
character of 1826 appears still more strikingly in the winter than it does in the 
summer season. 

The winter curve of 1826 bears a different relation to that of 1827 in its 
morning branch, but a similar relation to it in its evening branch. 



358 SIR DAVID BREWSTER ON THE HOURLY 



II. On the Arrangement of the Monthly Curves into three separate Groups. 

By examining the daily curve for each month, it will be seen that it preserves 
the general form of the daily annual curve, occasionally deviating into salient 
and re-entering portions ; but were we to delineate the individual daily curves, we 
should, in most cases, find the very form of a curve obliterated, and a capricious 
succession of elevations and depressions substituted in its place. 

The most remarkable result, however, is the distribution of the monthly curves 
into three separate groups, namely, curves of high temperature, such as those of 
June, July, August, and September; curves of low temperature, such as those of 
November, December, January, February, and March ; and curves of moderate 
temperature, such as those of April, May, and October. 

This distinct separation of the monthly group is well seen in the Plates XV. 
and XVI. of Volume X., which represents them as in 1824 and 1825. In that for 
1824 there is a very slight encroachment of the April curve upon that of January, 
but in that for 1825 the separation is complete. 

In 1826 and 1827 (See Plates XXIV. and XXV.) these curves are grouped, 
though less distinctly, according to the same law; but, what is very remarkable, 
the curve for January 1826 is entirely thrown out of the cold group, and in con- 
sequence of the extraordinary cold which prevailed in that month, its curve is 
as far separated from those of the winter group, as any one of the groups are 
separated from each other* 



III. On the Determination of the Tivo Hours of the Bay when the Mean Temperature 

occurs. 

Previous to the establishment of the hourly Register at Leith Fort, nothing 
was known respecting the times of the day when the mean annual temperature 
occurs. It was generally supposed to be about 8 o'clock in the morning, and 
Professor Playfair adopted this as the most probable result. With regard to 
the time when the annual mean occurred in the evening, I am not aware that 
even a conjecture had been formed. 

* The extraordinary character of the October curve in 1827 requires to be explained. When the 
daily schedules for that month were sent to me from Leith Fort, I was surprised to find two for the 
same day of October with very different numbers. Upon inquiring into the cause, I found that 
some of the non-commissioned officers who had voluntarily undertaken the duty of observing the 
thermometer, and for doing which they were liberally paid, had neglected to make the observations, 
and had filled up the daily schedules with false numbers. It is obvious from the curve that this 
fi'aud was committed by the person who made the afternoon and evening observations. 

It is interesting to observe how little effect these erroneous observations have had upon the 
general results for 1827, when compared with those of other years. 



METEOROLOGICAL REGISTER KEPT AT LE1TH FORT IN 1826 AND 1827. 359 





xioius oi moimug auu rjvemu 
Mean Temperature. 


3 Critical Interval 


In 1824 it occurred at 


f 9»» 13"> A.M. ) 

• \ 8 26 p.m. j" 


Hh 13m 


In 1825, 


J 9 13 A.M. \ 

' (8 28 p.m. j 


11 15 


In 1826, 


J 9 7 A.M. ) 
• |8 27 p.m.} 


11 20 


In 1827, 


J 9 12 A.M. ) 

• (8 23 p.m./ 


11 11 



Mean, ll h 15 m 



The mean of which is 



9 h ll m a.m. and 8 h 26 m p.m. 



The interval between the morning and evening mean temperature has been called 
the criticalinterval, which at Leith Fort is ll h 15 m , and which, there is reason to 
believe, is a fixed quantity. The equality of these numbers in four different years 
is very remarkable, the deviation of each from the mean not exceeding 4 m . 

Although the hours of mean temperature vary in different latitudes, and at 
different heights above the sea, yet the critical interval seems to be a fixed 
quantity everywhere, as appears from the following table : — 



At Padua, . 


ll h 


14m 


At Philadelphia, . 


ll h 


20' 


At Appenrade, 


11 


14 


At Belleville, 


11 


14 


At Inverness, 


11 


13 


At Trincomalee, 


11 


5 


At Tweedsmuir, 


11 


15 


At Kingussie, 


10 


44 



The mean of which is IP 10 m , differing only 4 m from the Leith result. 

The determination of the times of mean annual temperature gives us the two 
best hours for recording the indications of the thermometer, namely, 9 h ll m a.m. 
and 8 h 26 m p.m. ; for if any of the observations is accidentally omitted at one of the 
hours, the mean of the remainder will approach nearer to the mean temperature 
of the year than if any other pair of hours had been taken and similar omissions 
made. 

Another advantage of this determination is, that the mean temperature of the 
year may be obtained with great accuracy from a single observation made every 
day at one of the hours of mean temperature. 

If we examine the annual, or even the monthly, curves, it will be seen that the 
ascending, or morning branch, is more regular in its progression than the descend- 
ing, or evening branch, and therefore a single observation made at the time 
of the morning mean is preferable to one made at the time of the evening 
mean. 

This regularity in the morning curve has been observed in other phenomena, 
but especially in atmospherical polarisation, and the cause of it has been explained 
by Dove and Rubenson* 

* Memoire sur la Polarisation de la Lumiere Atmospherique, p. 86, note. 
VOL. XXIV. PAET II. . 5 E 



360 SIR DAVID BREWSTER ON THE HOURLY 

The hours of mean temperature have a considerable range in the monthly 
curves, varying in the morning from half-past 8 to half-past 10, and in the even- 
ing from 7 o'clock to 9. 

IV. On the relation between the Mean Temperature of the Day, and that of any single 
Hour, or pair of similar or homonymous Hours. 

It was long the practice of meteorologists to observe the thermometer at two 
convenient hours, so that if the one gave a temperature greater than the mean, 
the other might give a temperature as much less, and in this way several registers 
were kept with considerable accuracy. The hours of 10 h a.m. and 10 h p.m., sug- 
gested by the Rev. Dr Gordon, were frequently used, and gave a result nearer to 
the mean of the maximum and minimum than any other pair of convenient hours. 

Upon computing the mean temperature of every pair of similar or homonymous 
hours, I found, as shown in the following Table, that they differed very little 
from the mean temperature of the 24 hours : — 







Diff. from Mean 


Temp, of Day in 


Hours of Observation. 


Thousandths of a Degree. 






Leith. 


Inverness. 


5 h a.m. and 


5 h P.M. 


-0-134 


-0-434 


6 6 




-0281 


-0-543 


7 7 




-0372 


-0-552 


8 8 




-0421 


-0-396 


9 9 




-0-285 


-0-113 


10 10 




-0086 


+ 0174 


11 11 




+ 0176 


+ 0-374 


12 12 




+ 0-374 


+ 0-555 


1 1 




+ 0-367 


+ 0-550 


2 2 




+ 0-366 


+ 0-389 


3 3 




+ 0-252 


+ 0173 


4 4 




+ 0059 


-0-175 



Hence it appears that the defect or excess of the mean temperature of any pair 
of similar hours, when compared with that of the 24 hours, is always in the 
Leith observations less than half a degree. It appears, also, that the mean of 4 h 
and 4 h approaches nearest to the daily mean, and 10 h and 10 h next to it. 

I have added to the above Table the results of the Inverness hourly observa- 
tions. The deviations are very slightly greater, but the law is the same ; and it 
is interesting to observe the interchange of the signs at 10 h and 10 h , and 4 h and 4 h , 
a proof of the singular equality between the mean temperature of the day, and 
half the sum of the mean temperature of these hours. 

In speaking of this law, as given in the Report upon the Registers for 1824 
and 1825, Humboldt says, — 

" We are surprised, at the first glance, by the generality of this law. The 
homonymous hours are very inequally distant from the hour of the maximum of 
the daily temperature It is a thing truly remarkable, that from the 



METEOROLOGICAL REGISTER KEPT AT LE1TH FORT IN 1826 AND 1827. 361 

mean of two ordinates, we may deduce the mean temperature of the whole year ; 
that is, the mean of all the horary ordinates." 

As meteorological registers have sometimes been kept only once a day, it is 
desirable to ascertain the relation of the mean temperature of each hour to that 
of the day. In the following Table, I have given the results for 1826 and 1827, 
and also for 4 years, from 1824 to 1827 inclusive : — 



Hour. 
1 A.M. 


1826. 
-2-552 


1827. 
-L706 .. 


Mean of Four Tears 
1824-1827. 

—2-131 


2 


-2-903 


—2015 .. 


— 2396 


3 


-3-179 


-2-298 .. 


—2-658 


4 . . 


-3-228 


-2-308 .. 


— 2-793 


5 . . 


-3314 


-2-316 .. 


—2844 


6 


-2-943 


-2-011 


—2-545 


7 


-2-335 


-1-524 .. 


—1-956 


8 


-1-393 


-0-853 .. 


—1-180 


9 


-0-121 


-0-096 .. 


— 0-760 


10 


. +0-970 


+0-647 .. 


+0-777 


11 


. +1939 


+1-504 .. 


+ 1-702 


12 


+ 2-746 


+2-088 .. 


+2-463 


1 P.M. 


. +3-256 


+2-440 .. 


+2-865 


2 


+ 3-490 


+2-614 


+ 3-125 


3 


+ 3-473 


+2-536 .. 


+3-135 


4 


+ 3-411 


+2-353 .. 


+2-927 


5 


+ 3065 


+ 2028 .. 


+2-576 


6 


+•2-447 


+1-433 


+1-984 


7 


+ 1-442 


+0-845 .. 


+1-211 


8 


+ 0-383 


+0-350 .. 


+0-362 


9 


-0-460 
-0-964 


-0-304 .. 

-0-852 .. 


-0-410 


10 


—0-949 


11 


-1-432 


-1-044 


-1-351 


12 


-1-798 


-1-318 .. 


-1-713- 



From this Table it appears, that the mean annual temperature of any hour never 
differs more than 3i° from the mean temperature of the day for the whole year. 
The very same result was obtained from the Register of 1824 and 1825.* 

V. — On the Parabolic form of the Four Branches of the Annual Daily Curve. 

In the report upon the Register for 1824 and 1825, 1 have shown that the four 
branches of the annual daily curve approach so nearly to Parabolas, that the 
greatest difference between the observed and calculated temperatures is only a 
quarter of a degree of Fahrenheit. The following Table contains the calculated 
temperatures for 1826 and 1827, and the difference between them and the observed 
temperatures : — 



Edinburgh Transactions, vol. x. p. 387, 388. 



362 



HOURLY METEOROLOGICAL REGISTER KEPT AT LEITH FORT. 



Mean 



Min. 



Mean 



Max. 



Mean 



1826. 
48-468 
48-055 
47-375 
46-786 
46-287 
45-879 
45-562 
45-335 
45-199 
45154 
45-345 
45-918 
46874 
48-214 
48-468 
49-616 
50-641 
51-373 
51-812 
51-958 
51-874 
51-623 
51-203 
50-576 
49-861 
48-938 
48-468 



Difference. 

: 047 
-0-129 
-0-250 
-0-383 
-0-037 
-0003 
+ 0-046 
-0-041 
-0-000 
-0-180 
-0-215 
-0-201 
-0133 

0-000 
+ 0-178 
+ 0-234 
+ 0-159 
+ 0-088 

0-000 
-0-067 
-0-256 
-0-330 
-0-339 
-0-049 
+ 0-087 

0-000 



1827. 
48-423 
48-056 
47-522 
47-070 
46-700 
46413 
46-207 
46084 
46-043 
46-131 
46-396 
46-836 
47-453 
48-247 
48-423 
49-220 
50015 
50-583 
50-923 
51-037 
50-973 
50-780 
50-459 
50-010 
49-431 
48-725 
48-423 



Difference. 

-0-063 
-0049 
-0-309 
-0-405 
-0-304 
-0-201 
-0-041 

0000 
-0-024 
-0-015 
-0-063 
-0-117 
-0 080 

0000 
+ 0-150 
+ 0088 
+ 0-072 
+ 0-066 

0-000 
+ 0014 
+ 0004 
+ 0-008 
+ 0-154 
+ 163 
+ 0-052 

0-000 



From this Table it appears, that the difference between the observed and the 
calculated temperatures for 1826 and 1827, is only four-tenths of a degree of Fah- 
renheit, a very little more than in 1824 and 1825. 



I cannot conclude these observations, without directing the attention of the 
Society to the singular fact, that laws so regular as those we have been contem- 
plating should have shown themselves after only four years of hourly observa- 
tions. When we consider by how many disturbing causes the temperature at 
any particular instant is affected — by the winds which blow over surfaces differ- 
ently heated, — by the showers which instantly cool the air, — by the interposi- 
tion of clouds, now screening the sun, and now giving a free passage to his rays, 
and by many other causes, as capricious in their origin as they are irregular in 
their influence, it cannot but appear wonderful that all these effects should be so 
nicely balanced, as to produce a perfect compensation at every point of the 
annual daily curve. In virtue of this compensation, we may consider the mean 
annual daily curve as representing the mean daily progression of the solar heat, 
whether received directly from the sun, or returned into the atmosphere, by 
terrestrial radiation. 



( 363 ) 



XXVIII. On the Buried Forests and Peat Mosses of Scotland, and the Changes 
of Climate which they indicate. By James Geikie, Esq., of the Geological 
Survey of Great Britain. Communicated by Archibald Geikie, Esq., F.R.S. 

(Read 19th March 1866.) 

The following communication is an attempt to eliminate the geological history 
of our Scottish Peat Mosses. So much, however, has already been done in this 
matter, that the reconsideration of phenomena, for the most part well known, 
may appear almost a superfluous task. But, notwithstanding the essays of 
Walker, Rennie, Anderson, and others, in this department of geological inquiry, 
there is still probably much to be gathered from the same source, which shall 
greatly increase our knowledge of the condition of these latitudes in the ages that 
followed upon the close of the glacial epoch. At present, I mean to give only an 
outline of the subject, reserving for some future occasion a fuller statement of 
the facts on which the conclusions arrived at are based. 

Our peat mosses appear to contain the record of certain changes of climate, 
which have not hitherto fully engaged attention. The evidence furnished by 
the buried timber has indeed been frequently considered, but not so the proofs 
of altered conditions which the peat itself supplies. These last, more especially, 
form the subject of this memoir. But any paper treating of the origin and 
history of our peat mosses would be incomplete, without reference to the ancient 
forests which they cover, and the evidence on this head has therefore been 
recapitulated. 

It is proper to state here, that many observations on the present aspect of 
the peat of our hills and valleys were made conjointly by my colleague Dr 
Young and myself, during our survey of a large portion of the Peeblesshire hills. 
The subject of this communication was partially sketched out by us some time 
ago, but the pressure of other matters latterly deprived me of my colleague's co- 
operation. 

The phenomena revealed by our peat mosses are three-fold : — 
1st, The buried trees, and the condition of this country at the period of their 
growth. 

2d, The causes which led to the destruction of those trees. 
3d, The present aspect of the peat mosses. 
vol. xxiv. part ii. 5 F 



364 MR J. GEIKIE ON THE BURIED FORESTS 



I. Trees in Peat, — Condition of the Country at the Period of their Growth. 

It is well known, that below many peat mosses of this and other countries, 
the roots and trunks and branches of forest trees, and the remains of shrubs, are 
of common occurrence. Our Scottish mosses have yielded the oak, the pine, the 
birch, the hazel, the alder, the willow, the ash, the juniper, &c. ; but a greater 
number of species are dug from the peat of more southern latitudes. No one 
now doubts, that the vast majority of those trees and shrubs have grown in situ. 
And as there are few parts of the country where buried trees have not been dis- 
interred from peat or alluvium, the conclusion is forced upon us, that at some 
period in the past our island must have been exceedingly well wooded. Even 
the remote islands of the Hebrides appear to have had their groves of oak and 
pine. Throughout the bleak Orcades and sterile Zetland, large trees have at one 
time found a congenial habitat. Of the main-land it is difficult to say what district 
has not supported its great forests. The bare flats of Caithness, the storm-swept 
valleys of the Western Highlands, the desolate moory tracts of Perthshire and 
the north-eastern counties, the peaty uplands of Peeblesshire and the Borders, 
and the wilds of Carrick and Galloway, have each treasured up some relics of a 
bygone age of forests. 

It is much to be regretted, that in noting the occurrence of the various trees 
which our peat mosses have yielded, so little attention should have been paid to the 
relative elevation of the species above the sea-level. Enough is known, however, 
to assure us, that the pine and its congeners enjoyed a greater range in former times 
than at the present day. Mr Watson gives " 600 yards and upwards" as the 
elevation now reached by the Scotch pine. But he " has seen also small scattered 
examples at 800 and even 850 yards of elevation." These last, however, he thinks, 
had probably been planted. " But that the pine," he continues " has grown 
naturally on the Grampians, at an equal elevation in former ages, is rendered 
certain by the roots still remaining in the peat mosses of the elevated table lands 
of Forfar and Aberdeen, at 800 yards and upwards."* Again, in Glenavon, 
Banffshire, there are peat mosses, nearly 1000 yards above the sea, which contain 
abundant roots of the pine.f In the north of England, at the same height, "roots 
and trunks of very large pines are still seen protruding from the black peat." j 
Mr Watson says the Scotch pine now ranges from Perthshire into Sutherland, 
within latitudes 56-59°. § But in ancient times, it must have grown indiscrimi- 
nately throughout the length and breadth of Britain, as we meet with it in many 
of the English mosses, — those of southern as well as of northern regions. 

The common oak has a similar wide diffusion in our peat mosses. According 

* Cybele Britannica, vol. ii. p. 409. | Sinclaik's Stat. Ace. of Scotland, vol. xii. p. 451. 

J Mr Winch, quoted in Cybele Britannica, loc. cit. § Cybele Britannica, loc. cit. 



■ 



AND PEAT MOSSES OF SCOTLAND. 365 

to Mr Watson, it is now restricted to latitudes 50-58°, finding its northern limits 
in Ross, Aberdeenshire, and western Inverness-shire * But the peat mosses of 
more northern regions exhibit its decaying roots and branches ; and nothing is 
more common than to meet with trunks of oak, of very large dimensions, in situa- 
tions now in the highest degree unfavourable to the growth of that tree. Similar 
remarks apply to other species. But not only do the buried trees reach elevations 
unattained now by the same natural wood, they are also constantly dug out of 
peat mosses close to the sea-shore, of a size which rivals, or more frequently 
surpasses, that of their present representatives in Scotland, even when these are 
placed in situations most favourable to their growth.f 

Submerged Trees and Peat. — At various points along the sea-coast, observers 
have noted the occurrence below high- water mark of tree-roots fixed in a soil, 
and frequently covered over with peat moss. The shores of the Orkney and 
Shetland Islands, \ and the Inner and Outer Hebrides,§ furnish many interesting 
examples of these phenomena ; and along the coasts of the mainland || they 
are equally abundant. The " Submarine Forests" of England have long attracted 
attention. Few of the maritime counties do not exhibit them.^[ Around all the 
shores of Ireland drowned peat is of common occurrence. " At numerous points 
along the south and west coast it is a common practice for country people to go 
to the sandy bogs at dead low- water of spring tides, and dig turf from under- 
neath the sand ; and it has been equally noted in similar situations along the 
western and northern coasts. The stumps and roots of trees in the position of 
growth are found in this peat."** 

Again, on the further side of the English Channel, sunk forests abound along 
the coasts of Brittany, Normandy, and the Channel Islands. In those regions, 
trees have been observed at a depth which " could not have been less than 60 
feet below high- water." -j-f- The peat mosses of Holland, with their buried trees, 
are constantly continued outwards, so as to extend below the level of the sea. 
Thus, both on the east and the west shores of the German Ocean, we meet with the 



* Cybele Britannica, loc. cit. 

f Edin. Phil. Jour. vol. xvii. p. 53. See also Phil. Trans, vol. xxii. p. 980 ; and the Old and 
New Stat. Aces. Scot, passim. 

I Edin. Phil. Jour. vol. iii. p. 100 ; Sinclair's Stat. Ace. vol. vii. p. 451 ; Barrt's Orkney- 
Islands ; New Stat. Ace, Orkneys, Sandwich. 

§ Sinclair's Stat. Ace. vol. x. p. 373 ; vol. xiii. p. 321 ; Edin. Phil. Jour. vol. vii. p. 125. 

|| The Caithness coast shows submerged peat with trees, at Lybster and Beiss (from information 
by my colleague Mr B. N. Peach); for notices of submarine forests and peat, see a Practical Treatise 
on Peat Moss, p. 150 ; New Stat. Ace. vol. i. pp. 16 and 243 ; Sinclair's Stat. Ace. vol. xvi. p. 556 ; 
Trans. Boyal Soc. Edin. vol. ix. p. 419. Along the shores of the Firth of Forth drowned peat 
occurs, as at Largo ; also at several points on the Solway coast. 

% Phil. Trans, vol. xxii. p. 980 ; vol. 1. p. 51 ; vol. Ixxxix. p. 145; Jour. Geol. Soc. vol. vi. 
p. 96 ; Phil. Jour. April 1828. 

** Jukes' Manual of Geology, 2d edit., p. 686. 

ff Jour. Geol. Soc., vol. iii. p. 238. 



366 ME J. GEIKIE ON THE BURIED FORESTS 

same appearances as are found to characterise the margins of the English Channel, 
and the western and northern coasts of the British Islands. 

Tree-bearing Peat of Maritime Regions. — These facts, taken alone, prove a 
general loss of land. But, even without the evidence of the sunk forests, we 
should arrive at the same conclusion, after considering the nature of those trees 
entombed in mosses that occur close to our sea- coasts. The great size of the oak, 
and the dimensions attained by the pine, convince us that, during the period of 
their growth, those trees were far enough removed from the sea to escape its 
blighting influence ; in other words, that the land formerly extended farther 
seawards. When we turn to the trees of the submerged forests, we find them in 
like manner characterised by their large size. Hence, we are compelled to grant 
a still wider area for the old sunk country. 

No island of the Orkney or Shetland groups, can boast the presence of any 
natural trees deserving of the name. Cultivated saplings are protected by walls, 
but they cannot raise their tops above the level of the copestones. And yet the 
mosses and sunk forests of those regions abound with fallen trees, many of which 
equal in thickness the body of a man. When these buried trees decked the now 
bleak islands with their greenery, the land stood at a higher level, and the neigh- 
bouring ocean at a greater distance. A study of similar appearances in the 
Inner and Outer Hebrides will induce us to form a like opinion of the changes 
which they indicate. The broad barren flats of Caithness were also in ancient 
times overspread with a thick growth of large- sized natural wood, the peat 
mosses containing which pass below the sea. To have permitted this strong 
forest growth, we are again compelled to admit a former elevation of the land 
and a corresponding retreat of the ocean. And so on of all the maritime regions 
of Scotland. 

The same inferences may be drawn from the facts disclosed by the mosses of 
Ireland and England. On the coasts of France and Holland, as I have said, peat 
dips underneath the sea, and along those bleak maritime regions of Norway, 
where now-a-days the pine tree will hardly grow, we find peat mosses which con- 
tain the remains of full-grown trees, such as are only met with in districts much 
further removed from the influence of the sea.* 

Continental Britain. — Thus, over a very large area, we have proofs of a process 
of submergence which, to say the least, has materially diminished the extent of 
dry land in the north-west of Europe. From other evidence, which it is unneces- 
sary to recapitulate here, geologists have concluded that the area covered by 
the German Ocean, the English Channel, and the Irish Sea, has been at no distant 
date in the condition of dry land. After the deposition of the marine beds 
of the Drift Formation, a movement of elevation ensued, which resulted in the 

* From information obtained in Norway, 1865. 



AND PEAT MOSSES OF SCOTLAND. 367 

union of the British Isles with the Continent. The surface of this new land (over- 
spread with an undulating and profusely dimpled covering of drift deposits), 
abounded with lakes and pools. We have some grounds for believing, that at 
this period the climate was still cold enough to nourish glaciers in the higher 
valleys of our mountainous regions. Forbes has conjectured,* that at this early 
date our country may have been in the condition of the " barren grounds" of North 
America. But be that as it may, there can be little doubt, that at some time, 
during the latest great extension of the European Continent, the upraised beds of 
the Irish Sea, the English Channel, and the German Ocean, were included under 
the folds of that broad mantle of green forest, the relics of which are so con- 
spicuous in our peat mosses. 

It is certain, that at this time the oak and the Scotch pine were contempo- 
raneous throughout the greater part of Scotland. In the high-level mosses, the 
latter occurs most abundantly, while the former predominates in the peat of the 
lowlands. The pine does not appear to have formed any extensive forests at the 
lower levels of the country, although its remains have been disinterred from many 
lowland peat mosses.f Its choice of the more elevated regions was influenced, 
no doubt, chiefly by atmospheric conditions, but also in no slight degree by the 
nature of the soil. For underneath some low-level mosses, where oak forms the 
bulk of the buried timber, occasional large-sized pine trees are, as already 
remarked, not uncommon ; showing, that where the soil was favourable, the 
climate offered no great hindrance to their growth. It is in the hilly regions 
that the pine obtains that light gravelly soil which it prefers. At the lower 
levels, those drift clays and earths chiefly abound, which at a former period 
afforded a favourite habitat to the oak. 

Upon the whole, it must be conceded, that north-western Europe possessed 
at this period a climate more nearly approaching perhaps to that of the wooded 
regions of Canada, than to the climate which characterises Germany at the 
present time. The tough resinous wood and thick bark of our bog-pines bear 
emphatic testimony to the rigour of the seasons that nourished them. The 
present range of the pine in this country, as contrasted with its former wide dif- 
fusion, is also very significant. How changed the conditions which at one time 
permitted the increase of great conifers in the south of England and Ireland, but 
which now restrict their native growth to a limited area in the north of Scotland ! 

II. Causes of the Destruction of the Ancient Forests. 

Wind. — Some of the more apparent causes of the destruction of our ancient 
forests may now be considered. It is remarkable, that the trees below peat often 

* Memoirs of Geol. Survey. 

■ Vide Sinclair's Stat. Ace, and the New Stat. Ace. passim, and notices in various county 
histories, &c. 

VOL. XXIV. PART II. 5 Q 



368 MR J. GEIKIE ON THE BURIED FORESTS 

all lie one way, as if overturned by some potent agency they had met their fate 
at one and the same time.* The direction taken by the fallen trunks corresponds 
in a notable manner with that of prevailing winds in the regions where they 
occur ; and hence a large share in the destruction of our woodlands has been 
attributed to storms of wind. Doubtless, many acres of forest may have been 
overturned in this way. But we cannot suppose the peculiar position of the 
buried trunks to be in every instance the result of storms. Trees are usually 
bent over in the direction of prevailing winds ; and when any cause shall lead to 
their overthrow, whether it be natural decay or otherwise, the position taken by 
the falling trunks will be determined by the overhanging weight of their tops.f 

Lightning. — Again, in our own day, large tracts of forest land in the back- 
woods of America have been dismantled by fire, kindled during a thunder 
storm. And we may believe that the resinous conifers of the ancient Scottish 
woods may also have suffered from the same cause. The marks of fire are con- 
spicuous on the trees of some of our peat mosses. These appearances are to be 
traced chiefly to the hand of man, but we cannot quite ignore the possible agency 
of lightning. 

Ice. — It is not unlikely also that our ancient woods may have experienced 
what are known in America as ice-storms. In winter time the trees of the American 
forests sometimes become so heavily laden with snow and ice that they are borne 
to the ground by the pressure. 

Man. — That man has largely aided in clearing the woods is indisputable. 
Besides the evidence of his hand afforded by the charred wood under peat, we 
sometimes come upon marks of adze and hatchet. 

The earliest historical accounts of North Britain have afforded abundant food 
for controversy to antiquarians, but when the geologist has gleaned together the 
few descriptive remarks which occur here and there, in the pages of Tacitus, 
Heeodian, and others, he will find that his knowledge of the physical aspect 
of Scotland does not amount to much that is very definite. He will learn, 
however, that Caledonia was notorious on account of its impenetrable forests 
and impassable morasses. But the precise extent of ground covered by these 
woods and marshes must always be matter of conjecture. The forest land 
known as Sylva Caledonia? appears to have stretched north of the wall of Seveeus, 
but south of that boundary large forests must have existed ; indeed, down to 
much more recent times, many wide districts of Southern Scotland could still 
boast of their woodlands. Of the nature of those waste plains, described by the 

* Highland Society's Prize Essays, vol. ii. p. 19 (Old Series) ; Rennie's Essays, p. 31 ; Sinclair's 
Stat. Ace. vols. iv. p. 214; v. p. 131 ; and xv. p. 484; New Stat. Ace. Paisley and Carluke. 
Vide also for similar phenomena in English and Foreign peat mosses, Phil. Trans, vol. xxii. p. 980 ; 
Rennie's Essays, loc. cit.; Degner de Turfis, p. 81. 

t Vide Trans. Royal Soc. Edin. vol. iii. p. 269. 



AND PEAT MOSSES OF SCOTLAND. 369 

ancients as full of pools and marshes, we can have little doubt, although we 
cannot of course pretend to point out their particular site. Those who have 
traversed the central counties of Scotland, must have been struck with the num- 
berless sheets of alluvium which everywhere meet the eye, betokening the pre- 
sence, in former days, of so many little lakes. In Bleau's Atlas, many lochans 
appear in spots that have long ago come under the dominion of the plough. 
These, however, must form but a small proportion of the lakes which have been 
drained since the time of the Romans. Such inconsiderable peaty lochans were 
not likely to merit particular mention by the Roman legionary who had gazed 
on the Alpine lakes, save as they became vexatious interruptions to his progress 
through the country ; and surrounded, as many of them in all probability were, 
with treacherous morasses, the words of the old historians appear to have been 
descriptive enough of certain ample areas in the Scottish lowlands. 

It seems to have been the common practice of the Romans to cut down the 
trees for some distance on either side a " way," to prevent surprise by the enemy. 
Several old " ways" have been discovered on the clearing away of mosses, and 
in their neighbourhood lie many trunks of trees bearing evidence of having fallen 
by the hand of man. The presence of Roman axes and coins leaves us in no 
doubt as to who the destroyers were. Rennie has remarked,* that " of all the 
antiques found in mosses, by far the greatest part are Roman. No coins nor 
utensils of any other nation, so far as I know, at least none that would lead us 
back to a more remote period than the Roman invasion, have ever been dis-< 
covered." He is therefore disposed to limit the origin of much, if not the greater 
part, of our peat to the era of the Roman occupation. It need scarcely be added, 
that since Rennie wrote, many relics of human art have been disinterred from 
the peat mosses of Scotland and other countries, which archaeologists agree in 
considering to be of much more ancient date than the Roman invasion. But it 
is quite evident, that such imbedded relics do not enable us to fix the age of a 
peat moss. They merely tell us, that the origin of the peat cannot date back 
beyond a certain period, but may be ascribed to any subsequent time.f Hence, it 
is impossible to say what amount of waste we are to set down to the credit of the 
Romans. Some authors have, perhaps, been too ready to exaggerate the damage 
done by the legions. The buried forests which can be proved to have fallen before 
Roman axe and firebrand are not many after all ; but we may reasonably suppose 
that these form only a portion of the woods which were cleared at that time. 

We have, however, what appears to be direct evidence, to show that some 
regions had been divested of their growing timber before the Roman period ; for 

* Essays, p. 69. 

t It appears not unlikely that the fact of several mosses having yielded remains of undoubted 
Roman age, may not infrequently have weighed with local antiquarians in assigning to the same era 
certain relics of no marked character, which have occasionally been discovered under peat. 



-°>70 MR J. GEIKIE ON THE BURIED FORESTS 

if Solinus may be trusted, the Orcades were, in the days of the Romans, bare 
and bleak as they have been ever since. He says, " Numero tres, vacant homine, 
non habent silvas, tantum junceis herbis inhorrescunt, csetera earum nudae 
arenae et rapes tenent." A patriotic Orcadian might insist that the statement 
"numero tres" renders what follows untrustworthy; and perhaps he might 
prefer the testimony of Ossian, who, in his poem of Carric-thura, says of 
some island in the group, " a rock bends along the coast with all its echoing 
wood." According to Torfaeus (historiographer to the King of Denmark),* the 
condition of the Orcades in the year 890 agreed with the description given 
by Solinus. f For at that time Einar conferred a great boon upon his country- 
men by teaching them the use of peat for fuel, enim in Orcadibus non erant 
sylvce. Yet it is well known that the peat mosses of the Orkneys, and even 
those of Zetland, contain the remains of considerable trees. 

The limits of this communication will not permit me to consider in detail 
accounts of the condition of the Scottish forests in times subsequent to the Roman 
period. Any reference by the chroniclers to the state of our woodlands is only 
incidental, and perhaps not always to be relied upon. It is interesting, however, 
to learn from Boethitjs, that the horrida Sylva Caledonia? had in his time become 
mere matter of history. J He further tells us, that Fifeshire had formerly been 
well wooded (in the times of some of his early Scottish kings) ; but " it is now," 
says his old translator, " bair of woddis ; for the thevis were sometime sa fre- 
quent in the samin that they micht na way be dantit, quhill the woddis war bet 
down."§ Again, Boethius describes the island of Isla (whose peat mosses con- 
tain roots and trunks of trees) to be an island rich in metals, which could not be 
wrought on account of the want of wood. [J 

After the period to which Boece refers, any allusions to the aspect of the 
country are best sought for in cartularies and such records. For the rights 
acquired by monasteries over various forests throughout the country, these car- 
tularies afford abundant evidence. Chalmers^" has enumerated many instances 
of special grants by kings and barons " of particular forests in pasturage and 
panage, and for cutting wood for building, burning, and all other purposes ;" and 
Mr Tytler** has added to the list. It need hardly be remarked, that the greater 
part of these woodlands has long disappeared. And yet, according to Chalmers, 

* Torfaeus wrote about 1690. He was a native of Iceland, and died in 1720. 

f Solinus is supposed to have written about a.d. 240. 

J If this had not been the case, he would surely have quoted a less ancient authority than 
Ptolemy for the site of the ancient forest. Vide Cosmographie and Description of Albion. 

§ Croniklis of Scotland, chap. xi. 

|| Bellenden's version of the passage is characteristic. He says, Isla is " full of metallis, gif 
thair wer ony crafty and industrius peple to win the samin ;" but he quietly drops all allusion to the 
want of wood in the island. 

Tf Caledonia, vol. i. p. 792, &c. 

** Hist, of Scot. vol. ii. chap, ii., third edition, and the authorities there quoted and referred to. 



AND PEAT MOSSES OF SCOTLAND. 371 

the old cartularies " abound with notices of forests in every shire during the 
Scoto-Saxon period." I have not hesitated to quote the authority of those 
records, and the opinions of two such learned and correct writers as Chalmers 
and Tytler. No one can deny that the evidence of the cartularies is in 
favour of a better wooded condition for the country than now obtains. But 
we must guard against the mistake of supposing that all the area embraced 
under the designation of a " forest" was covered with forest trees. And there can 
be little doubt that both Chalmers and Tytler read the cartularies in the light 
of the facts which are disclosed by our peat mosses. The trunks of pine, oak, 
ash, and other hard timber dug out of the mosses, were regarded as proofs that 
the regions indicated by the cartularies were in reality the sites of great forests 
at the time to which those records refer. But it is probable, nay, in many cases 
quite certain, that much of this buried timber belongs to a more remote period . 
But even with this reservation, Scotland, down to the fourteenth century, would 
appear scarcely to have merited the description given by ^Eneas Silvius at a 
later date. During the civil commotions of the country, and the long wars with 
England, much wood seems to have been destroyed, and the gradual progress of 
cultivation also began to encroach upon the forest lands. Another cause which 
aided in clearing away the woods from some portions of the maritime districts, 
is to be found in the great number of salt-pans that were early established in 
Scotland, and the right which the proprietors usually obtained to cut the requisite 
firewood from the forests of the country. But although wood appears to have 
been the fuel commonly employed in the manufacture of salt, yet it is not 
unlikely that peats may also have been burned in some cases. It is certain, 
at least, that peat was a common enough fuel in David I.'s reign, and that, as 
Chalmers says,* " petaries became frequent objects of grant to the abbots and 
convents during the Scoto-Saxon period." This fact ought perhaps to be looked 
upon as a further proof of the increasing decay of the forests. 

But by far the most remarkable testimony to the bare condition of the country 
is furnished by the Acts of the Scottish Parliament. From the times of the First 
James, stringent acts were adopted by successive Parliaments,! having for their 

* Caledonia, vol. i. p. 793. 

f Vide Acts of Scottish Parliament. The more interesting acts referring to the state of the 
woods were passed as follows : — James I., Second Parliament, a.d. 1424 ; James II., Fourteenth 
Parliament, a.d. 1457; James IV., Sext Parliament, a.d. 1503; James V., Fourth Parliament, 
a.d. 1535; Mary, Sext Parliament, 1555; James VI., First Parliament, 1567, Sixth Parliament, 
1579, Eleventh Parliament, 1587. It is curious to notice how, from the time of James I. the 
penalties imposed upon the destroyers of wood increase in severity. Pecuniary fines are succeeded 
in time hy stocks, prison, or irons ; the culprit is to be fed on bread and water during confinement, 
and to be scourged before parting from his jailers. The climax is reached in the following 
act, which became law in 1587 : — -"Whatsoever persone or persones wilfully destroyis and cuttis 
growand trees and cornes, sail be called therefore before the Justice or his deputes, at Justice Airs, 
or particular diettes, and punished therefore to the death, as thieves." 

VOL. XXIV. FART II. 5 H 



372 MR J. GEIKIE ON THE BURIED FORESTS 

object the preservation of the woods. JEneas Silvius (afterwards Pope Pius II.), 
who visited this country about the middle of the fifteenth century, relates, 
" Pauperes pene nudos ad templa mendicantes, acceptis lapidibus eleemosynse 
gratia datis, laetos abiisse conspeximus. Id genus lapidis sive sulphurea sive alia 
pingui materia praeditum, pro ligno, quo regio nuda est, comburitur."* Such a 
statement regarding the bare condition of the country might have been thought 
somewhat exaggerated, for it is the testimony of a visitor from more favoured 
climates ; but its truth is curiously illustrated by the wording of an Act of 
Scottish Parliament, passed in the reign of James IV. : — " Anent the artikle of 
greenewood, because that the Wood of Scotland is utterly destroyed, the unlaw 
theirof beand sa little : Therefore," &c.f 

There are, of course, numerous traditions regarding the former wooded con- 
dition of various districts from which the trees have long since been stripped. 
Many of these refer to some of those woods which I have already mentioned, as 
being frequently named in the cartularies and similar records. 

Another line of evidence is supplied by local names ; but into this subject I do 
not enter here. 

The short outline of historical facts given above seems to prove — 

1st. That when the Romans entered Britain they found the surface of the 
country to some extent covered with forests, but diversified in many places with 
bogs and marshes. 

2d. That to this period we must refer the destruction of some portions of the 
ancient forests, whose remains are dug out of our peat mosses ; but what amount 
of damage the woods then sustained we have no means of ascertaining. 

3d. That from the time which elapsed after the departure of the Romans, 
down to the eleventh century, we have no certain records referring to the state of 
the preservation of any part of the Scottish woods, if we except the statement of 
Boethius, who tells us that Fife had in great measure been divested of its forests 
by some of his early Scottish kings. 

4th. That from the eleventh to the thirteenth century, and down even to 
later times, there appear to have been still considerable areas of forest land, 
the rights to which were frequently granted to ecclesiastical communities and 
others. 

5th. That during these centuries much forest was thus cleared and brought 
under cultivation ; that at the same time woods were exhausted by building and 
burning, more especially as fuel for the salt-works ; while extensive tracts were 
displenished and laid waste during times of war and civil strife. 

6th. That from the time of James I. there appears to have been a progressive 
decay of the remainder of the Scottish woods. 

* De Europa, c. 46. f Sext Parliament, a.d. 1503. 



AND PEAT MOSSES OF SCOTLAND. 616 

Having alluded to some of the more obvious causes which have aided in the 
overthrow of our ancient forests, I shall now proceed to discuss what I consider 
to have been the chief agents in the work of destruction. For this purpose it is 
necessary that the more striking peculiarities exhibited by a section of a work- 
able peat moss should be here borne in mind. 

The best peats are " cast" towards the bottom of a peat moss. They show a 
somewhat close and compact texture, so much so as occasionally to resemble 
coal. Above this the peat begins to lose its more compact structure, and vege- 
table fibres may be detected, which on a closer inspection are recognisable as 
those of a moss. Towards the upper portions of the section this appearance 
becomes still more conspicuous, and the peat seems to consist almost entirely of 
mossy fibres. Throughout the section long grasses may be seen, sparingly in 
the lower portions, but becoming more abundant as we near the top, where twigs 
of heather begin to mingle with them. The upper surface or crust of the peat 
moss (a foot more or less in thickness), seems to be made up chiefly of heather 
and grasses, and such plants as Polytrichum. When peat moss wants this crust, it 
generally shows a treacherous surface covered with moss, into which the unwary 
pedestrian may sink deeper than he might have expected. Small areas of this 
nature are not uncommon, but they may be considered as exceptional cases. 
Most peat mosses are provided with a crust of heath and grass. This crust is 
termed " heather-," and sometimes " hill-peat," from its common occurrence on the 
slopes and summits of hills, where it does not necessarily overlie true moss peat. 
It seldom exceeds a foot or two in thickness, and ought properly to be considered 
as turf rather than peat. 

The compact nature of bottom peats is due to mineralisation. But another 
variety of peat bog appears to show that vegetable matter, the tissue of which 
has been nearly lost, may be deposited in a peculiar manner under water. The 
mosses in which this process takes place are termed in Scotland "flows," a kind 
of bog characteristic of the peat of the low grounds.* The surface of a flow moss 
is usually flat, or nearly so, frequently showing dark lochans or tarns, the appear- 
ance of which gives us the key to the history of the flow. Their examination is 
attended with some inconvenience, owing to the instability of the peat, which, 
when ventured upon, will sometimes rise and fall with a disagreeable undulating 
motion. The peat, in short, is a mere pan or crust spreading over and concealing 

* I have, however, observed flow-mosses on the flat col between two hills, and they are also 
common enough in some valleys, where we have no reason to suppose that they mark the site of 
lakes. The origin of" flows" in such situations is due to the presence of springs. " Grass and 
weed," says Dr King, " grow rapidly at the outburst of these. In winter, these springs swell and 
loosen all the earth about them ; the sward, consisting of the roots of grasses, is thus lifted up by the 
water. The sward grows thicker and thicker, till at last it forms a quaking bog." In the same 
manner, " flows" are often extended beyond the limits of the lakes which they cover, by the out- 
welling of the imprisoned water during wet seasons. 



374 MR J. GEIKTE ON THE BURIED FORESTS 

a sheet of water, portions of which are seen in the dark lochans referred to. 
Many flows, however, do not exhibit tarns, and these, during wet seasons, when 
the underlying reservoir has received the surplus drainage of the moors and 
mosses, are liable to swell up and burst. It is not difficult to see how the sub- 
jacent lake has acquired its covering of peat ; for in the gaps of this covering we 
can watch the process of bridging-over the dark inky water in full operation. 
Creeping out from the edges of the peat, a thick growth of Sphagnum and various 
aquatic plants gradually encroaches upon the limits of the tarns. As this out- 
growth becomes denser, rusty grasses begin to steal over its surface, and bright 
tufts of Polytrichum also find there a congenial soil. So the process goes on until 
a crust, firm enough to support such plants as cranberry, bog myrtle, and hea- 
ther, eventually makes its appearance ; but while the upper surface of this crust 
or cake of peat thus solidifies and thickens, its under portion rots and falls down 
as a black vegetable sediment upon the lake bottom, where it slowly accumu- 
lates, until in time the depression occupied by the lake may come to be filled up. 
Many of our deeper peat mosses appear to have had such an origin. 

There are thus two kinds of peat — 1st, That which is due to the continuous 
upgrowth from the soil of Sphagnum and its allies ; 2d, Flow-moss peat. The 
mode of formation of a " flow" is sufficiently evident, but the origin of the other 
peat mosses cannot always be so readily made out. It is from these last that the 
buried trees have been dug, and hence it has commonly been thought that the fall 
of the trunks, by obstructing the drainage, allowed moisture to collect and form 
a marsh, in which bog-mosses sprung up. The overturning of the timber is thus 
considered to have been the proximate cause of the formation of our peat mosses. 
That much peat may owe its origin to such a process is certain, and several cases 
are on record where the changes referred to have been observed in progress. But 
this does not seem to have been the exclusive, or even the most frequent, cause 
of its formation. There are many peat mosses in which no decayed ligneous 
matter whatever can be detected. In the hilly districts of Southern Scotland, peat, 
made up almost entirely of mosses, with the usual capping or crust of heather 
peat, is of common occurrence, even on considerable hill slopes. While in the 
majority of cases, where the peat of the higher flat-topped hills in the same region 
is found to contain ligneous remains, the roots and branches are often of small 
size, indicating the presence in former times of a scraggy brushwood. Now, if* 
bog mosses could of themselves find sufficient moisture to enable them to form 
peat on a slope of 25°, it is unnecessary to suppose that they must have awaited 
the overthrow of mere brushwood before they could begin to grow on a flat 
hill top. It must therefore be allowed that some peat mosses at least have 
originated without the aid of fallen timber to collect moisture for their sup- 
port. 

Those peat mosses, however, which exhibit the trunks of large trees, bearing 



AND PEAT MOSSES OF SCOTLAND. 375 

marks of fire, or adze and hatchet, may be considered to have had their growth 
materially aided, if not always primarily caused, by the obstruction of the pros- 
trate trees. But the peat bogs which have supplied such proofs of human agency 
bear only a small proportion to the mosses where no such traces have been 
detected. In most cases, both roots and trunks tell distinctly their story of 
natural decay. In the many mosses which I have visited, the trees were invari- 
ably found in such a state as plainly showed that natural decay had preceded 
their overthrow. 

Are we to suppose that the peat only began to grow after those trees had thus 
yielded to decay ? Did the fall of the trees, by choking the drainage, only then 
bring about the requisite conditions for the increase of Sphagnum and its allies ? 

In a favourable climate, trees, which have given way before tempest or old 
age, are quickly replaced by seedlings, and thus the gap caused by their over- 
throw is gradually filled up Why then, we may ask, was not this the case with 
the ancient forests of Scotland ? It seems strange that the death of the trees, 
instead of being succeeded by the appearance of another generation, should 
invariably give rise to a peat moss. The explanation of this anomaly ought to 
be attributed to a change of climate. From some cause or other, the conditions 
requisite for the continuous growth and succession of forest trees no longer existed 
to the same extent. The nature of the great trees embedded in many of our peat 
mosses points, as already remarked, to the former prevalence, over these regions, 
of a somewhat excessive or continental climate ; and (following other authors) 
I have sought to connect this period with the continental condition of Britain that 
followed upon the close of the glacial epoch. Ere long certain changes ensued, 
with a marked effect upon the vegetation. The succession of trees revealed by 
several peat mosses seems to warrant us in concluding that the severity of the 
climate which had nourished the hardy Scottish pines began at length to give 
way. The most obvious cause of this change must be referred to the new geogra- 
phical position of the country. The gradual separation of these lands from the 
continent must have been followed by as gradual an amelioration of climate. 
Whether, apart from the changes arising from oscillations of level, there may not 
have co-existed some cosmical cause sufficient of itself to have brought about an 
alteration of climate, can only be conjectured in the present state of the evi- 
dence.* 

It is worth noting that the succession of trees revealed by some English peat 

* I have confined my remarks on this subject to the peat mosses of our own country, where 
the appearances presented may be explained, as stated above, by a change from continental to insular 
conditions. If, however, the alteration of climate referred to was also in great measure due to cos- 
mical causes, the proofs are no doubt to be found in continental peat mosses. As I do not know 
these turbaries from personal observation, I am unable to say whether the greater proportion of 
their buried timber has fallen from natural causes or otherwise. It may be surmised, however, that 
'narks of natural decay will probably occur most abundantly in the maritime regions. 

VOL. XXIV PART II. 5 I 



376 MR J. GEIKIE ON THE BURIED FORESTS 

mosses does not quite tally with that which is said to characterise the peat of 
Denmark. In the Danish peat mosses the pine lies at the bottom, and is succeeded 
in ascending order by the oak and beech. But in the bogs of England, oak and 
pine occur, as in Scotland, on the same horizon, and in such a way as to show 
that they must have grown contemporaneously in the same forest, the pine occu- 
pying the higher levels and more gravelly soil. Above the oak and pine we often 
find a second stratum of timber, consisting chiefly of birch and hazel. When, over 
this, we come upon a third layer, its prevailing wood is generally alder*. Occa- 
sionally, however, pine trees are met with in peat mosses at a lower level than 
oak.f While it is not denied that in this succession of trees we may have evi- 
dence of certain changes of climate, we ought to be careful that we do not attach 
too much importance to what may in many cases be only a local accident. The 
succession of trees may sometimes be explained by a change in the nature of the 
soil alone. Thus, in some of those clayey depressions in the drift, which have 
been occupied at one time by the oak, we have evidence of a subsequent irruption 
of fresh water converting the grove into a marsh. When the oaks had succumbed 
to these changed conditions, we find them succeeded in place by some other 
species, such as the alder or willow : from which it does not seem necessary to 
infer more than a mere local change of circumstances. This peculiar succession 
of trees, however, appears to have so frequently recurred in the peat mosses of 
England (if not in those of Scotland), that we are forced to conclude that pheno- 
mena so general in their appearance must be due to some common and widely 
acting cause. 

But, apart from the evidence supplied by a succession of trees, the geologi- 
cal history of the peat mosses themselves is conclusive upon this point. The 
phenomena they present indicates the former prevalence of an extremely humid 
climate. During the continental period the atmosphere must have been moist 
from excess of vegetation, but in the succeeding or insular condition this humi- 
dity appears to have greatly increased. At what time such a climate first began 
to characterise these regions, it is of course impossible to say ; but probably long 
before the complete submergence of the area now covered by the German Ocean, 
those changes had already been set in progress, which, in the course of ages, were to 
result in the formation of many, if not by far the greater portion, of our peat mosses. 

The most continuous sheets of peat occur on the west side of our island, and 
this fact is to be connected with the greater rainfall of the west as compared with 
that of the east coast. It was over this rainy region that peat would first begin 

* Vide Timber Trees, Society for Diffusion of Useful Knowledge, p. 32. 

| Mr Sainter, in a letter to my colleague, Mr A. H. Green, describes the Danes' Moss, a 
large peat bog near Macclesfield. In this moss, he says, " the Scotch fir is found at a depth of 
about 20 or 25 feet. A few feet above this lies the larch, and then in ascending order come the 
oak (Quercus Robur), birch, hazel, alder, and willow." This moss occupies a depression. 



AND PEAT MOSSES OF SCOTLAND. 377 

to spread itself. In the lakes and pools of the country, Sphagnum and other 
aquatics had luxuriated from an early period, covering the surface of the water 
with an unstable crust, which often-times gave way beneath the weight of large 
quadrupeds, such as the Irish deer. Many old lake hollows, long since filled up 
with peat, teem with the relics of this and ot